"Of course we need to return to winning ways," said the Scot.
"We need to try and get ourselves to be hard to play against and get something out of the good play we have in games."
United were knocked out at the third-round stage for only the second time in 30 years when Wilfried Bony's 90th-minute winner
earned Swansea a first win at Old Trafford
after Javier Hernandez had cancelled out Wayne Routledge's early goal.
The hosts' misery was compounded by a sending-off for defender Fabio Da Silva 10 minutes from the end after he had replaced Rio Ferdinand, who suffered a knee injury in his first game since 10 December.
The defeat, United's seventh of the season in all competitions, came after they were
beaten 2-1 by Tottenham
at Old Trafford on New Year's Day.
Man Utd's home struggles
Manchester United have lost four of their last six home games in all competitions
The Red Devils have kept just one clean sheet in their last six at Old Trafford
United have scored more than one goal in just one of their last seven games at home
United midfielder Darren Fletcher said the team "had let Moyes and the fans down".
"It's a massive blow, let's not kid ourselves here, this is a really bad result and there are a lot of angry, hurt players," the Scottish midfielder added on MUTV.
"It's not good enough and we're going to have to raise our performance levels."
United were without injured strikers Wayne Rooney and Robin van Persie, while Moyes also rested midfielder Michael Carrick and centre-half Nemanja Vidic ahead of Tuesday's Capital One Cup semi-final first leg at Sunderland.
"We have another big game in 48 hours so we have to keep that in mind, but there is no excuse really, we had a very strong team," added Moyes. "Just about every player on the pitch was an international player.
"We shouldn't [rely on Rooney and Van Persie]. It should be that we put out a really strong team, everybody gets their opportunity to show what they can do, and then I make decisions from that."
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