Liverpool opened the scoring just before half time thanks to a Daniel Sturridge strike, but Sevilla levelled 17 seconds into the second half and never looked back.
It was a desperately disappointing night for Liverpool - and despite Liverpool's heroics at Anfield in this competition - yet again the big final experience saw them wilt.
The reds switched off in the second half of the Europa League final - ending any hopes of a 9th European trophy.
Klopp picked his strongest side available but on the night it just wasn't strong enough - not at least for the full 90 minutes.
Alberto Moreno had a horror show - at times in the second half it wasn't clear if he knew which team he was supposed to be playing for.
Liverpool started slowly in the first half but grew into the game and ended the first half looking the stronger side.
It was Daniel Sturridge who broke the deadlock - a hit with the outside of his left foot that sailed into the net.
— Liverpool Gifs (@LiverpoolGifs) 18 May 2016
Within 17 seconds of the restart however, Liverpool's familiar failings were exposed as Kevin Gameiro waltzed into space in the Liverpool defence to level. He headed in a cross from Mariano Ferreira after poor work from Alberto Moreno.
The reds never got going.
Coke put Sevilla ahead just after the hour with a fine strike from the edge of the box, and five minutes later - Can gave the ball away then a poor touch from Coutinho split our own defence allowing him to wrap the game up.
Despite sending on Origi and Benteke Liverpool never looked likely to get even one goal back.
The reds now have runners up experiences in every domestic and European competition since the win in Istanbul - and for Klopp it was his 5th consecutive final defeat.
There were some disappointing decisions by the referee - at least one of three handballs in the area by Sevilla should have been punished - and Dejan Lovren saw a header ruled out due to Sturridge being offside.
On another night more fuss may have been made of this - but the reds were so abject in the second half that it was barely worth mentioning.
Liverpool miss out on European football next season
MOTM: Kolo Toure