Liverpool lost 3-1 despite having led through a brilliant Daniel Sturridge strike as they fell apart in the second- half , with neither the players nor their manager able to do anything to halt the decline.
It was a chastening experience for all but particularly Klopp who, having inspired a remarkable comeback against Borussia Dortmund in the last eight, has now lost his last five finals.
His credentials are not in question as the progress made since he took over from Brendan Rodgers in October is evident but that will not stop the German analysing himself - before turning the spotlight on his squad.
“The first thing you have to do when you look at the man in the mirror is criticise yourself,” he said.
“As manager of the team all I have to do is self-criticise, nothing else. It is all about us, all about me. It is my job to help the players to react in different situations better. I can improve a lot.”
Despite some encouraging performances this season there has been a lack of consistency while the Reds have reached two finals in quick succession and not won either, losing February’s Capital One Cup final to Manchester City on penalties.
Having not utilised the January transfer window to bolster his squad Klopp has already signed Schalke centre-back Joel Matip and Red Star Belgrade midfielder Marko Grujic for next season - and there will be more arrivals to come over the summer.
But after an exhausting 63-match campaign there will be no European football next season and that will benefit Klopp as he seeks to properly stamp his mark on the club.
“It is clear we are not in a European tournament next year so we don’t have football on Wednesday or Thursday so we will have time to train and we will for sure come back stronger,” he added.
“Of course this team will be a little bit different next year but we will do something with transfers first.
“Hopefully the players all come back (from Euro 2016) healthy and we have no injury problems for pre-season.
“It will be a long tournament for my players, some of them could stay in it for a long time and then only have a short break.”
Prior to the match against Sevilla Klopp and his players had insisted they had learned from their League Cup final defeat to City.
After being completely over-run in the second-half at St Jakob-Park with no response the manager knows there is still some way to go on the education front.
“We need to use the experience because I am sure we will again be in a final and we will have decisive moments and if we do we will react better,” he said.
“They are still young, this was the players’ first big final, but unfortunately it is the second time [they have lost a final] this season.
“We will use this experience together and then some day everyone will say Basle was a very decisive moment in the future of Liverpool.”
Klopp was particularly unhappy with the way his side reacted to conceding an equaliser to Kevin Gameiro just 18 seconds into the second half.
The instant abandonment of what he has been trying to instil in them since the first day he took over was a worry and game-management is also something else which has to improve. But the Reds boss stressed there was no magic wand he could wave to cure their ills in one fell swoop.
“We have had a lot of moments this season when we have played good football and known how to protect situations but if you saw at 1-1 we passed through small channels and lost the ball and you cannot protect situations like this,” he said.
“We have to do it more often, we have to work on it. It is not a wonder it is pure work and that is what the job is.”