United have wobbled at the top of the table following back-to-back defeats against Liverpool and Fulham which has seen their lead reduced to a solitary point.
The reigning champions do have a game in hand and Giggs is remaining upbeat despite the lacklustre 2-0 loss at Fulham at the weekend.
"We're obviously disappointed with the result," Giggs said. "After losing last weekend, we wanted to come here and put on a good performance.
"We didn't do that in the first half – our passing was sloppy and our movement wasn't good enough. We just couldn't get it going, the tempo wasn't good.
"Going a goal behind and down to 10 men, we had to arrange our shape a little bit differently. We came out and played a lot better in the second half.
"We were on top, we created some good chances and their keeper made a couple of good saves. Had one of those efforts gone in then we could have gone on to win it but it wasn't to be.
"Some of our lads now go away for the international break. Hopefully we won't have any injuries and we can get back on track against Villa."
Though Liverpool closed to within a point of United by beating Villa 5-0 on Sunday, fellow title rivals Chelsea also slipped up after a 1-0 defeat at Tottenham.
Giggs was surprised by Chelsea's setback at White Hart Lane, but says the United players are not worrying about the results of their pursuers.
He added: "We didn't expect that result. it's better than them winning.
"We've got to do our own job, not worry about the teams around us. It's still in our hands."
United's assistant manager Mike Phelan meanwhile has denied the club have a disciplinary problems after both Wayne Rooney
and Paul Scholes were sent of at Craven Cottage.
Rooney in particular appeared agitated by referee Phil Dowd's decision, but Phelan insists the pressure is not getting to the Old Trafford contingent.
"Am I concerned about indiscipline? No, we'll take care of our own house. We are good at that," he said. "Our players will be reflecting on their performances. They have got 10 days to do that. They go away for their internationals and they will come back with a clear mind.
"We felt that Wayne was trying to get on with the game. He got the ball and threw it back to his own player. I don't think it was near the referee.
"It just seemed very trivial, maybe not in the referee's eyes, but in our eyes it seems a trivial thing to do."