It took four attempts, butJurgen Klopp finally secured the first win of his Liverpool tenure on Wednesday night, with his side defeatingAFC Bournemouth 1-0 to advance to the quarter-finals of the League Cupand, having tasted victory, the German can use a strong run in this domestic competition to build towards glory.A Nathaniel Clyne goal was enough to secure progress on a decidedly muted Anfield night, while heroics from Adam Bogdan between the sticks ensured the impressive Junior Stanislas didn't spoil Klopp's cup debut.A trip to take on Ronald Koeman's Southampton awaits in the next round, and after drawing with the Saints in the Premier League earlier this month, Klopp will be confident he can go one better this time.With his first campaign on Merseyside a low-expectation improvement mission, success in the League Cup could prove the perfect milestone on his quest to restore Liverpool to top-level status.Positive Signs at AnfieldWith three draws in his first three games as Liverpool manager, the signs of progress under Klopp were small but growingly significant, with improvement in the Reds' shape off the ball and their increased work rate showing the steps the German has taken in implementing his philosophy.Fielding a 4-2-3-1 formation at Anfield, Klopp saw his side dominate in attack, with Roberto Firmino, Joao Carlos Teixeira and Jordon Ibe all impressing in support of lone striker Divock Origi.Firmino was crowned Man of the Match, and the Brazilian's tenacity, technical quality and tactical awareness saw him operate on a level above any other player on the Anfield turf.Though he failed to get his name on the scoresheet, Firmino inspired Liverpool to victoryit was his immaculate through ball that initiated the move prior to Clyne's 17th-minute strikeand Klopp will be hoping the 24-year-old will play a key role as he builds on this victory.After the game, he told reporters how he was "really satisfied," as relayed by the club's official website:I feel much better than after a draw.But I dont think the other games were so much worse than todayof course, the result is the biggest difference and we did well tonight.We didnt have too much time again between the games, not too much time for training, only one hour training with this new team and new system.I saw minute by minute we were better in the game, we closed the spaces better and the whole 90 minutes we played football and created our chances. We didnt have any real experience together, so Im really satisfiedthe boys did really well.Though the Reds were lining up against relatively lowly opposition in Eddie Howe's Cherries, with the 37-year-old forced into a number of changes due to injury concerns and a necessary focus on Premier League endeavours, this victory showed Liverpool are heading in the right direction under Klopp.Like Howe, Klopp will no doubt regard progress in the league as more important in his first season in the English top flight, but at Anfield on Wednesday he will have recognised the benefits of the League Cup.The Benefits of the League CupHeading into Wednesday night's clash, Klopp made nine changes to the side that drew 1-1 with Southampton on Sundaylikely with one eye on preserving the fitness of his key players ahead of Saturday's trip to Stamford Bridge to take on Chelsea.This saw only Clyne and Origi retain their place in the German's starting lineup, with fringe players Bogdan, Kolo Toure, Dejan Lovren, Joe Allen and Ibe given a chance to impress alongside Firmino, who made his first start since recovering from a back injuryhis first start under Klopp.Furthermore, Klopp handed full debuts to three of his young stars: Teixeira, Connor Randall and Cameron Brannagan.For Brannagan, 19, and Randall, 20, this represented an immense opportunity, as theIndependent's Simon Hughes explained following the Reds' victory:The respective rises to this night, where both made their full Liverpool debuts, is a mark of determination and development as well as circumstance.Brannagan and Randall had trained so well at Melwood over the past few weeks that the Liverpool manager, Jurgen Klopp, felt he knew to whom he could turn when numbers in his squad were low.Both performed with distinction on the night, with Randall in particular growing in confidence as the match played out, showcasing his ability to pair passion and defensive strength with consistency in the attacking sector, and the Liverpool-born full-back can be hopeful of a regular role under Klopp this season.Teixeira, too, did little to harm his first-team chances in a display hallmarked with clever flicks, well-timed runs and attacking intent, while Ibe could well have secured a starting role against Chelsea with his intelligent performance on the right flank.It is this progress in the squad ranks that makes the League Cup such an invaluable competition, with Klopp pairing a hungry youth with old hands who have a point to prove, and this can only aid his side elsewhere.There was no feeling of contempt in Klopp's rotated selection, with the German stressing before the game, as reported by the Press Association (h/t This is Anfield), that "I make the changes not because this competition is not important for me, [but] because I want to win the game," but as Hughes continued, he may begin to focus more heavily on the League Cup after this win."Having lifted just one trophy in the last nine yearsthe most barren period of time the club has experienced in more than half a century," Hughes suggested, "Klopp may soon decide this is a competition that is worth prioritising."With Chelsea, Arsenal and Manchester United all suffering defeat to lowly opposition in this round, and only Manchester City remaining of the Premier League's top-level clubs, this represents a perfect opportunity.Springboard to SuccessThroughout Brendan Rodgers' spell in charge on Merseyside, the universal goal of "top four and a trophy" proved alarmingly elusive, underlined by the Reds' failure to progress beyond the semi-finals in both the League Cup and FA Cup last season.Defeat to Aston Villa in the Reds' all-important Wembley clash in April consigned Rodgers' final full season at Anfield as an undisputed failure, with Tim Sherwood's side wholly outfoxing their opposition.This loss signalled Rodgers' inability to mastermind cup glory, with similar disappointment in European competitions throughout his tenure further highlighting thisit was a lack of experience that undermined his time in charge, and Rodgers was arguably unable to build due to these regular disappointments.Klopp, however, boasts considerable pedigree on this stage, having won the DFB-Pokal once with Borussia Dortmund, as well as reaching the Champions League final in 2013.Though the 48-year-old was forced to rotate his side on Wednesday night, it is clear that he is aiming for success in every competition this seasonif possible."We set out trying to win every single tournament that we are in, so we want to try and get the win, progress to the next round and hopefully we can go all of the way in the competition," Clyne told the club's official website before the game."We want to keep pushing to try and finish as high as we can in the league and hopefully we can bring home a trophy for the fans."The right-back reinforced this in his post-match interview with Sky Sports, concluding simply that "we're footballers and we always want to win."In these early stages, Klopp's arrival on Merseyside is as much about restoring belief as it is achieving success, and Clyne's confidence post-match highlights the effect the charismatic German is having on his squadLiverpool are desperate to win.Clyne's suggestion that securing silverware is "for the fans" is particularly pertinent, with recapturing the ferocity of Anfield key to improvement on the field, as sickly notions of fortresses and 12th men are undeniably important.A strong cup run can ensure Klopp gets off on the right foot, benefiting both his squad and his supporters.Though the League Cup is typically derided as a subpar competition, Klopp should not ignore the virtues of success, even on this lowly stage.It could be the first step towards long-term glory.Follow @jacklusby_ Click here to read full news..