With the team currently 12th in the Premier League, the Europa League offers a chance for redemption.
United are unbeaten and fourth in their group, and a win over FCSB on Thursday would secure a spot in the last 16.
"The most important thing for us is to win," Onana said.
"As a Manchester United player, we know how important that competition is.
"For me, we have to win the Europa League. For the guys, they all know it's a big opportunity for us to go directly into the Champions League, so we will give everything to win the Europa League.
"If we fail, it's not good, because it's something we definitely have to win and we will give everything to win.
"It will not be easy, because some opponents are very good, and that's why we’ve drawn some games against very good opponents in the past.
"But the mentality and the standard is always high. So any competition we will step in to play, we have to win, and the Europa League is one of them, so we'll go there with the winning mentality, to play the last game in Bilbao.
"We already know where the final is (Bilbao), so we have to be ready to give everything and try to win the Europa League because it's very important for us, not only the Europa League but also in the FA Cup and in the Premier League we have to try to finish as high as we can."