Brendan Rodgers' men crashed out of the competition on penalties on Thursday at the hands of Besiktas, Dejan Lovren missing the crucial spot-kick to end the last 32 tie.
But goalkeeper Mignolet insists sixth-placed Liverpool are desperate to bounce back as attention switches to Manchester City's visit to Anfield on Sunday.
On Liverpool's top-four prospects as the club seek a return to the Champions League, Mignolet told the Liverpool Echo: "Of course we can do it.
"We always said we want to get in the Champions League for next season.
"We're still in the FA Cup and we're close to the top four in the Premier League so there is still a lot to play for this season.
"It's not easy at this moment when you've just come out of the dressing room and we've gone out of Europa League but we have to put it behind us.
"Everyone is devastated to go out, especially like that at the end of 120 minutes.
"We have to look forward and prepare ourselves as best we can. We need to recover and then go again on Sunday.
"It's another big game and we need to try to get back to winning ways. We have to focus on the job in hand."
Mignolet, who confirmed that Liverpool practice penalties every week in training, refused to blame Lovren, as he added: "I've always said when you win, when you lose, when you go through, when you go out, it's always as a squad."
