Jose Mourinho admitted that Sunday’s 2-0 defeat to Arsenal means it will now be "impossible" for Manchester United to finish in the top four.
United remain four points adrift of fourth-placed Manchester City with three games remaining, including a trip to second-placed Tottenham Hotspur.
Mourinho said their cramped schedule, which includes a possible two further Europa League games, means they must win the tournament to qualify for next season’s Champions League.
"It is impossible to finish in the top four. We must play Thursday (against Celta Vigo) and then we go again against Tottenham, but we cannot go with everything against Tottenham," the United manager said.
"Three days later we have Southampton, and then Crystal palace. Others will be playing once a week."
Mourinho said he was delighted with the performance of his players and said, under the burden of so many injuries and fixtures, he was surprised they managed to go 25 games unbeaten in the Premier League.
He said his task now was to continue to rotate his squad to ensure United win the Europa League. At the Emirates, Mourinho gave a Premier League debut to Axel Tuanzebe, saying he was delighted by the 19-year-old’s performance.
"The kid was brilliant," said Mourinho, who asked him to play at right-back instead of his normal position in the centre of defence.
"Tuanzebe is a good player. He is a good kid and a good professional and it doesn’t matter what position he starts. Every minute he spends with us training is fantastic for him, every minute in the Premier League is a plus.
"To play against (Alexis) Sanchez, (Mesut) Ozil, (Danny) Welbeck... these are big players. His best position is central defence but against the big boys it is right-back."
Jose Mourinho accepts top four finish for Manchester United is impossible