Michael Laudrup's side were beaten 4-1 by the defending Premier League champions, with United strikers Robin van Persie and Danny Welbeck netting a double apiece at the Liberty Stadium.
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And captain Williams, who has been linked with a move to Arsenal, believes they can do just that.
"It doesn't feel nice and I think confidence does get rocked a little bit," said the 28-year-old, in quotes reported by WalesOnline.
"The gaffer said not to let exactly that happen, but I think it's only natural.
"We're disappointed, but it's the job of the older boys to pick the squad up.
"The good thing is that we've got a game coming up so we can't dwell on it for too long."
Next up for Swansea is the visit of Romanian outfit Petrolul Ploiesti in the UEFA Europa League play-off round on Thursday.