Man United will enter Thursday's second leg at Old Trafford currently 2-0 behind on aggregate.
De Gea, however, has claimed that "anything is possible" with the Red Devils and has vowed that the players will put on a show for the supporters.
"With United, anything is possible. That's one of the great qualities of this club, we always believe and always fight until the end. We believe in ourselves and we believe we can be in the next round," De Gea told United Review.
"We didn't play to our best last week, that's clear and they had a lot of chances and possession. But now we have a chance to put things right at home. We need to improve in all things – both defensively and attacking. We need to fight hard, be aggressive and show our passion. We need to show why we are Manchester United.
"We know we have the quality and we have the belief, and we want to make it a special night for our fans who support us no matter what."
Man United will resume Premier League action with a trip to Manchester City on Sunday afternoon.