Everton manager David Moyes saw his side crash out of the Europa League but hopes they can recover and seal a place in the competition next season.
At least that would be some consolation after second-half goals from Miguel Veloso, Pedro Mendes and substitute Matias Fernandez gave Sporting Lisbon a 4-2 aggregate victory and a place in the last 16.
Moyes said: "We will do our best. It is a long shot at the moment. But will try to do that again."
Holding a 2-1 advantage from the first leg and on the back of a superb victory against Manchester United, Everton were widely expected to complete the job in Portugal.
However they hardly had a shot on target, a surprising statistic considering they went into the match in a good run of form after only two defeats in 13 matches in all competitions.
Moyes said: "We never got started. Credit to Sporting, they were the better team and deserved to go through.
"We felt confident but maybe we made mistakes in the first game which let them in. They took their opportunities.
"I didn't see this result coming. We didn't play to the levels we have in recent weeks. They worked very hard and ran very hard all night. The idea was to go and get a goal. But we found it difficult. We knew the opening 20 minutes would be tough. But we never made anything happen."
Everton suffered another injury setback with centre half Phillipe Senderos limping off in the second half after he had suffered a back problem. He was replaced by Phil Jagielka, making his first appearance since April following a knee injury.
Moyes said: "We do not think it is too serious regarding Senderos but we are not sure. It was good to have Jagielka back and he will help us towards the end of the season."