Sevilla lifted the Europa League trophy for a third successive season by beating Liverpool 3-1 in the final in Basel, Switzerland, on Wednesday night.
Liverpool squandered the chance to end an 11-year European drought, while Sevilla qualified for next season's Champions League group stage despite finishing seventh in La Liga.
Daniel Sturridge's exquisite first-half goal would have been worthy of winning any UEFA showpiece, but manager Jurgen Klopp's side failed to capitalise and went to pieces in the second half.
Kevin Gameiro scored just seconds after the interval as the Reds were exposed defensively before Coke grabbed two in the space of six minutes to end Liverpool's dream of a return to the gloried European nights of yesteryear.
Emre Can had the first shot of the match in the eighth minute, with goalkeeper David Soria pushing the ball away to his left.
Then Sturridge had an effort, but he couldn't hook a shot into the net from Nathaniel Clyne's pass, and a defender cleared from inside the 6-yard box.
Sturridge then had another chance in the 25th minute, but Soria came out to smother his effort.
Sevilla got their first real chance on the half-hour, as Kevin Gameiro went inches wide with the overhead kick.
Liverpool found the breakthrough in the 33rd minute, and it was Sturridge with a wonderful finish. He received the ball just inside the area and beat Soria with a superb, curling effort with the outside of his left foot that bent inside the opposite post.
Liverpool thought they had a second five minutes later when Dejan Lovren headed in from a corner, but Sturridge, in an offside position, attempted to get a flick on the ball and the flag went up.
The Premier League side were dominant now, in search of a second before half-time, but they had to be content with a one-goal advantage.
But all Liverpool's hard work was undone just 18 seconds after the restart as Sevilla levelled. Mariano skipped past two defenders before superbly squaring for Gameiro, who couldn't miss from 5 yards out.
Two minutes later and Gameiro was through on goal. He looked certain to get a shot away until he was caught by Kolo Toure, who made a vital last-ditch tackle to snuff out the danger.
Sevilla were bossing the second half, and Gameiro missed another chance on the hour -- Steven N'Zonzi's flick on dropped for the striker but goalkeeper Simon Mignolet managed to force the ball over the bar.
And they got their reward in the 64th minute: Coke with a fine finish from the edge of the box to turn the tie on its head.
The Spanish side's outstanding comeback was complete five minutes later as Coke notched his second -- with a huge slice of luck. The ball took a double-deflection of two Liverpool players and ran to the unmarked Coke, who managed to beat Mignolet. Liverpool protested furiously, but at no point was there a moment when Coke could have been offside.
Klopp threw on strikers Divock Origi and Christian Benteke, switching to three at the back, in a desperate attempt to effect a miraculous comeback to match that over Borussia Dortmund in the quarterfinal second leg at Anfield, but this time his magic touch failed to deliver.
Liverpool could find no way back, and Sevilla once again celebrated on the European stage.