Holding a 2-1 advantage going into the second leg, they were given a chasing by a rejuvenated Sporting side.
Second-half goals from Miguel Veloso, Pedro Mendes and
susbstitute Matias Fernandez sent the home side through to the last 16.Sporting midfielder Pedro Mendes felt his side deserved to book a tie with Atletico Madrid in the last 16.
"We needed this win," former Portsmouth and Rangers midfielder Mendes told Five.
"We wanted to progress in this competition. I think we performed really well in the first leg, we were unlucky with the result.
"Today we did what the gaffer asked - patience. We knew we couldn't concede or it would be very tough for us.
"We've been a little unlucky (recently). It's exactly the same in the league here - we've been struggling for results. We needed this performance today."
Everton boss David Moyes felt Sporting were in control virtually from kick-off.
"We didn't play well enough," Moyes told Five. "From the start Sporting got a grip of the game, put us under pressure.
"I thought we'd weathered it before half-time but we never caused them enough problems."
EVERTON BOW OUT OF EUROPA LEAGUE
