Ander Herrera's third Premier League goal gave United the lead just before the half-hour mark, but Swansea quickly drew level through Ki Sung-yueng.
The visitors piled on the pressure in the second half but lacked a clinical touch in the final third, and they paid the price as Jonjo Shelvey's 73rd-minute shot deflected off Bafetimbi Gomis to secure three points for Swansea.
Rooney was frustrated at seeing his side lose a game he felt they should have won easily, putting their place in the top four in jeopardy.
"Of course, it is hard to take," he told MUTV. "Certainly, in the second half, I thought we dominated up until they scored and I thought we got a great goal to go 1-0 up.
"In the second half they were struggling to get out but then they hit us with a sucker punch, a shot from 30 yards and a deflected goal. These things happen but it was a disappointing day for us.
"As I said before, I thought we dominated but maybe didn't test the keeper enough up until they scored, that's disappointing given the play we had.
"It was one-way traffic and it felt like that on the pitch, it felt like a matter of time. We were putting them under pressure but they did defend the box well, putting bodies in front of the ball, but this is a blow for us, coming away from today with no points having played like that."
United will look to bounce back next weekend at home to Sunderland, although they could start that match outside the top four if Southampton beat Liverpool on Sunday.
