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  The Reds led at the interval only to suffer a second-half collapse as Sevilla became the first team to win the competition three seasons in a row.
  The defeat means Liverpool will not play any European football next season.
  "It was 50-60% of our usual quality and we have to accept that," said Klopp, who took charge at Anfield in October.
  "I am responsible for this performance. I promise everybody we will use it and come back stronger."
  Liverpool were on course to secure Champions League football - on offer to the winners of the competition this year - when Daniel Sturridge's magnificent strike with the outside of his left foot gave them the interval lead.
  But the Reds conceded three goals in the space of 24 second-half minutes - Kevin Gameiro netting 17 seconds after the interval, before Coke struck twice.
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  "There is no criticism and I have spoken to my players," added Klopp.
  "What I think about not being in the Champions League is that we have to use the time.
  "It is not about the size of the squad, it is about using the time in training to get better."
  Former Liverpool defender Mark Lawrenson was frustrated by the Reds' second-half collapse.
  "Experience was key after conceding," said the 1984 European Cup winner, who was part of BBC Radio 5 live's team in Basel.
  "Where was the central defender or captain saying 'circle the wagons for 20 minutes - we do not concede and we get ourselves back into game'? That is something Liverpool just didn't do.
  "They had one stonewall penalty in the first half but when you go in 1-0 up at half-time in a cup final, what is the first thing anyone says in the dressing room?
  "You make sure you don't concede in the first 10 or 20 minutes. What did Liverpool do? They conceded in the first 17 seconds."
  Left-back Alberto Moreno was at fault for Sevilla's first goal, and Lawrenson was also critical of the 23-year-old's performance.
  "Yet again Moreno, who used to play for Sevilla, has made a massive mistake," he said.
  "I've lost count of how many mistakes this guy has made.
  "It's all very good pouring forward but the clue is in the title - left-back. Try defending occasionally. Moreno has made mistakes all season - basic errors.
  "Where was he for Villarreal's goal the other week? He was trying to score a goal at the other end."
  Lawrenson said former Liverpool boss Brendan Rodgers, who was sacked in October, had to share the blame for not strengthening the left-back area during his tenure.
  He added: "Liverpool didn't have, by the end of August, another player who could play left-back unless they moved Nathaniel Clyne from the right.
  "Jose Enrique was never going to play. I'm sorry, Brendan Rodgers gets the blame for me."
  Lawrenson expects a summer of change at Anfield, but expects Sturridge and Brazilian duo Roberto Firmino and Philippe Coutinho to stay.
  "I'd imagine Liverpool have spoken to agents and will have an indication of whether players are coming," he said.
  "If you are in a room with Klopp then I'd think it was hard to say no to him. This summer's transfer window is going to be the biggest ever in the Premier League in terms of money spent.
  "Firmino, Coutinho and Sturridge are not going anywhere this summer - other than on holiday.
  "Klopp knew within two weeks of taking over he needed to bring in players.
  "Why didn't he address it in January? He probably did but could not get the right personnel in."
target: Liverpool boss Jurgen Klopp took responsibility for his side's 3-1 Europa League final defeat by Sevilla - and said they would come back stronger.