Jose Mourinho's side meet Rostov at Old Trafford in a good position to reach the last eight, having secured a 1-1 draw in the first leg last week.
United are locked in a tense battle to finish in the top four of the Premier League this season, as they lie in sixth place in the table and six points adrift of fourth-place Liverpool, although they have two games in hand.
With victory in the Europa League final in May perhaps offering their most realistic route of a return to Europe's top competition, Fellaini is determined to respond to Monday's FA Cup exit at the hands of Chelsea with a victory on Thursday.
"Monday was a hard game for us at Chelsea - 10 players for one hour," Fellaini told a press conference. "It was difficult to win the game. But we lost, now we look forward. It is important we win the game.
"It was a long trip [back from London] but we are professional. We know how to recover. We trained a little bit yesterday, a nice recovery. We will be ready.
"All the players, staff and supporters want to be in the Champions League next season so we will do everything to be there. We have the squad and the players, we are confident. Everyone will see that against Rostov. We are confident.
"We have played good teams in Europe. In the Premier League, every game is tough. Every game is difficult. We have to take it game by game.
"We have had a lot of games, played all the competitions but all the players are ready to play. We have good fitness, we have good staff, a good recovery department so we are all ready. That's football - to play a lot of games."