Jose Mourinho said Manchester United would fight for a top-four finish in the Premier League until it was "mathematically impossible" after a 3-0 victory at Sunderland on Sunday.
Goals by Zlatan Ibrahimovic, Henrikh Mkhitaryan and Marcus Rashford eased United to a vital three points after drawing six of their previous nine Premier League games.
They are unbeaten in their last 21 league games but Mourinho's side, who moved above Arsenal into fifth place, are still four points behind Manchester City with a game in hand.
Liverpool, in third place, are six ahead of United having played two games more.
"We want to fight in the Premier League until it is mathematically impossible. The Premier League we cannot win, but Europa League we can," Mourinho said.
"We had lots of players that were not here today and the most important thing after the three points was to have no more injuries. The result was good. We resisted the results of yesterday when Manchester City and Liverpool won."
United, who are in the quarter-finals of the Europa League, were without first-choice goalkeeper David de Gea but his deputy Sergio Romero had an easy afternoon in the Sunderland sunshine.
With a Champions League spot available for the winners of the Europa League, that is arguably their more likely route back into the elite competition and they face a quarter-final, first leg at home to Anderlecht on Thursday.
They then host Premier league leaders Chelsea next weekend.
Mourinho said Romero would play against Anderlecht.
"(De Gea) has a problem with his hip. When he dives he feels it a little bit. It's good for him to have a rest," Mourinho said. "It's good for Sergio Romero to play before Anderlecht.
"De Gea will probably be fit for Chelsea."
Sunderland manager David Moyes said his side would keep fighting, even if they look doomed.
They have equalled the second-worst run of Premier League games without a goal having not scored for seven games and are 10 points adrift of 17th-placed Hull City.
"We keep going. We have another home game next Saturday and we have to try and win it," Moyes said.
"We do some good things but just lack a bit of quality but it's not for the want of trying.
"The boys are doing everything they can."
(Reporting by Martyn Herman, editing by Pritha Sarkar)