Sevilla survived a first-half battering before hitting back with three second-half goals, two from Coke, to beat Liverpool 3-1 in the Europa League final on Wednesday and win the trophy for the third season in a row.
Liverpool dominated the early stages and went ahead through an exquisite goal by England striker Daniel Sturridge, who nonchalantly curled an inswinging shot inside the far post with the outside of his left foot.
Sevilla clung on until halftime and hit back dramatically when Kevin Gameiro turned in Mariano Perreira's cross less than one minute after the re-start.
Coke fired Sevilla ahead and added a controversial third after the linesman initially raised his flag for offside, only for referee Jonas Eriksson to award the goal following a lengthy consultation.
"This is our competition. We did an amazing second half. I am so proud of our team mates, the supporters. It was an amazing night," Sevilla defender Daniel Carrico said after his team secured a place in next season's Champions League.
"Liverpool were really good in the first half. The manager said we had to change our game, to believe. We did what he said. In the second half Liverpool didn't have any chances," he added.
Sturridge seemed to have set up a Liverpool win when he gave them a 35th-minute lead with a strike which was reminiscent of Brazilian Ronaldinho at his best.
The goal inspired a superb spell from the Premier League team and they should have scored a second when Nathaniel Clyne fired a low cross across the face of the goal but nobody made contact.
The Spanish side equalised almost immediately from the re-start when Alberto Moreno headed a clearance straight to Mariano who burst to the byline and produced a low cross which was tapped in by Gameiro.
The Frenchman was put through again two minutes later and, although Kolo Toure got back to block his shot, Liverpool were suddenly on the ropes.
Vitolo set up Sevilla's second in the 64th minute when he exchanged passes with two players before Coke sped in from nowhere to fire a low shot past Simon Mignolet from the edge of the area.
Six minutes later, Ever Banega found Coke who scored again amid furious protests from Liverpool whose coach Juergen Klopp rushed down the touchline to confront the match officials.
"We have showed throughout the competition that we are good enough to win it, but we didn't on the night that mattered most," Liverpool captain James Milner said.
Liverpool will not now play in a European competition next season.
"Massive blow for a club of our stature. We have been in two finals this season but not managed to get over the line," Milner said, referring to Liverpool's League Cup final loss to Manchester City on penalties.
"We were ready for the second half but gave away a sloppy goal and never really got back in the game," Milner said.