Seb Larsson's goal in the 30th minute condemned the outgoing champions to their seventh home league reverse this term, and was the Black Cats' first win at United since 1968.
United's miserable form cost David Moyes his job last month, with Giggs appointed on an interim basis until the end of the season.
It had looked as though a corner had been turned with the 4-0 victory over Norwich last weekend, but many old failings returned as United struggled to break down a determined Sunderland side.
Giggs told Sky Sports: "I'm just disappointed, more than angry. We just didn't show that quality that we showed last week, especially in the final third. When you do that you come unstuck in the Premier League.
"I just didn't think that there was that concentration today when the passes really mattered.
"When you've got to break open a defence, play that key pass, or concentrate on a finish, it just wasn't there.
"I said last week we want to make it (Old Trafford) a fortress, as it always has been a difficult place to come. This season that has been the problem, our home form hasn't been good enough.
"The quality wasn't there. Once Sunderland got that first goal they got everyone behind the ball and counter-attacked on us, but we had enough possession to create more chances than we did.
"Manchester United is a big club. The form hasn't been good enough this year. I'm sure there will be players coming in, quality players. We need to improve and do better next season."
Giggs has pledged to continue to rotate his squad for the final two games of the season, and hopes Wayne Rooney will have recovered from a tight groin in time to face Hull City on Tuesday.
He added: "Hopefully his groin will settle down and Wayne will be involved, but we're just monitoring it.
"I said I'd give everyone a chance before the end of the season and that's what I'll carry on doing. I still believe in the quality in the dressing room."