Sebastian Larsson scored the only goal of the match on the half-hour mark to give the visitors' chances of Premier League survival a huge boost.
But Giggs - in interim charge of the Old Trafford club for the second game - admitted his disappointment at the standard of his side's display.
"I still believe that there's quality in the dressing room and we showed that last week (4-0 win against Norwich City), we just didn't this week," he said. "Whether it be lack of confidence or concentration, I honestly don't know.
"There was a lack of quality in the final third. First half, we got some decent crosses in, we just didn't get enough people in the box.
"Second half, we had all the possession and just couldn't find that key pass or that bit of quality that would have got us back in the game.
"I'm sure if we'd have scored one, we'd have gone on to score a few more.
"Lack of quality and lack of concentration in the final third."
And Giggs feels United, who parted company with former boss David Moyes last month, have suffered as a result of their poor home form this season.
"We've shown good form away from home, but at Old Trafford seems to have been the problem this year," he continued.
Giggs also paid tribute to Gus Poyet's visitors, who are now three points clear of the relegation zone, with two matches left to play.
"Sunderland are on a great run, credit to them today, and against decent opposition you need to produce consistent performances and that's what's lacked this year," he added.
