Manager Michael Laudrup says four of Swansea's next five games are against "tie-break opponents" in their bid to survive in the Premier League.
The Swans face Fulham, West Ham United, Cardiff City and Stoke after a 19 January clash at Tottenham Hotspur.
Speaking after his side's he said: "In those games we have to pick up points."
However, Ki Sung-Yueng will not return from his Sunderland loan spell to aid 13th placed Swansea.
The South Korean scored his third goal in eight games in Sunderland's 4-1 at Fulham on Saturday.
"There is a possibility to bring him back but I don't think it is a good idea," said Laudrup.
"Ki feels comfortable where he is now. If we take him back, he would not play every game.
"Mentally, it would be very bad for him."
Defeat at Old Trafford came seven days after Swansea's first ever win there,
Antonio Valencia and Danny Welbeck struck after the break as the hosts exacted revenge.
Laudrup said: "Manchester United were very focused because of what had been said and written in the last days.
"We expected them to come out from the first moment and want to get on top.
"I don't think that happened. We coped very well.
"What really hurt us - and we talked about it at half-time - was the first 20 minutes of the second half.
"We conceded after 90 seconds."
Laudrup says the setback has changed nothing in his outlook on the task ahead for his side.
He added: "It is true we have to improve the level of performance, like another nine or 10 teams.
"We are still in the same position. I said before the competition started there are 11 or 12 teams in a relegation battle.
"After the Tottenham game we have Fulham, West Ham, Cardiff and Stoke.
"They are the tie-break opponents for us. In those game we have to pick up points."