Jurgen Klopp has urged Liverpool to turn their recent improvement into a season-saving revival as the Reds eye Champions League revenge against Real Madrid.Klopp's side are showing signs of finally emerging from a dismal spell that threatened to ruin their entire campaign.Liverpool have reeled off successive victories over Everton and Newcastle to give them renewed hope of snatching a top four finish in the Premier League.Saturday's 2-0 win at Newcastle moved Liverpool to eighth in the league standings, within six points of the fourth-placed Magpies with a game in hand.While it is too early to say Klopp has found remedies for everything that has ailed Liverpool throughout a traumatic season, they welcome Real to Anfield for Tuesday's last-16 first leg with morale no longer at rock bottom.Klopp will take that as a foundation from which to kick-start Liverpool's bid to win the Champions League for a second time under the German.Liverpool, six-time winners of Europe's elite club competition, would already have more Champions League triumphs in the Klopp era if not for pesky Real.The Spanish giants beat Liverpool in the 2018 final, eliminated them in the 2021 quarter-finals, and won last season's final 1-0 in Paris, thanks to Vinicius Junior's goal.Liverpool haven't beaten Real since a Champions League last-16 victory in 2009.Last year's loss was especially painful at the end of their failed quadruple chase, a quest that brought just FA and League Cup success and left Klopp's players struggling mentally and physically this season.Even greater scars were worn by the Liverpool fans traumatised after police used unnecessary force in ugly scenes outside the Stade de France before kick-off in the Champions League final last year.