United had a red card for defender Victor Lindelof overturned by VAR and Marcus Rashford pulled a goal back in added time but there was no time left to mount a comeback and they fell to a second defeat in a row for the first time since Ole Gunnar Solskjaer took over as manager in December.
United are set to enter the global break sat outside the Champions League spots. It's the poorest performance since I've come here.
"It was a big step backwards I have got to say", said Solskjaer.
United will return to action on Saturday 30 March with an important Premier League match against Watford at Old Trafford, with a victory clearly needed in the fight to finish in the top four. It's very disappointing that we're not in the semis.More news: Sling them out or long delay: Europeans weigh Brexit options
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"You're always measured on results but we played a good game against Arsenal", he told a media conference. Once the worldwide break is over, United will need them back to their best providing a cutting edge required to negotiate a hard run-in over the final eight league games.
"You can't sit and sulk too long", he said. "This week we did get what we deserved because we never deserved to win this game". We've got so much to play for.
Speaking to reporters, Solskjaer spoke and referenced his former manager, United great Sir Alex Ferguson, saying: "It's the not squeaky bum time like the gaffer used to say but it tightens up and April and May at Manchester United is when we narrow the focus and it's now about winning trophies, making use of the squad".
"So, there's so many things that we need to think about". "When they come back again, we'll give it a good go".