Alex Ferguson's second placed side head to leaders Chelsea for Sunday's summit meeting having managed just three clean sheets in 12 matches this season.
Although United have won 10 of the last 11 games in all competitions, they have conceded four times in the last two after gifting their opponents head starts.
Stoke were allowed to go 1-0 up at Old Trafford last Saturday before losing 4-2, while Portuguese side Braga sailed into a 2-0 lead in Manchester on Tuesday before losing 3-2 in the Champions League.
While United escaped with victories from those two matches, Giggs knows a team of Chelsea's quality are far more likely to take advantage of such sloppy play.
"That's probably the biggest disappointment from this season, the number of times we've gone behind," United midfielder Giggs said.
"On the plus side, though, we've managed to come back in the majority of those games and win them.
"Obviously we can't go throughout the season like we have been doing.
"But we know that if we get clean sheets and we start getting zeros against our name then we'll create chances at the other end and win more games than we lose."
Giggs is pushing for a return to the starting line-up as United look to reduce Chelsea's four-point lead at the top.
The former Wales international, who turns 39 next month, made an 11-minute substitute appearance against Braga but is desperate to start against Chelsea after setting his sights on a 13th Premier League title medal.
"I'm in good shape," said Giggs, who has been used sparingly by Ferguson this season. "I was at the Olympics so I missed the majority of the pre-season training we do.
"That meant I was perhaps a little bit behind in relation to other players. But I've managed to get that back in order over the last few weeks, working with the coaches. I feel good at the moment."
Shinji Kagawa will miss the Chelsea game after the Japanese midfielder was ruled out for up to a month with a knee injury.
Goalkeeper Anders Lindegaard is out with a thumb injury while long-term absentees Nemanja Vidic (knee), Phil Jones (knee) and Chris Smalling (metatarsal fracture) remain sidelined.
Chelsea's flying start to the season was shattered by the midweek Champions League defeat at Shakhtar Donetsk, but their outstanding Premier League form ensures they face United with no shortage of confidence.
A return of seven wins and a draw from their opening eight games means Roberto Di Matteo's side will remain top whatever happens on Sunday, but a victory over the closest rivals would clearly be a major boost to their title challenge.
Di Matteo admits his side were affected by the defeat in Donetsk, but the Italian believes United's defensive frailties ensure the European champions go into the game with plenty of belief they can bounce straight back.
"I always pay attention to the mood in the camp and certainly after the defeat in Shakhtar it is not the best in the dressing room, but we can show and prove we are strong team," Di Matteo said.
"United are conceding a few goals and we have a big threat as well, we will try to exploit those weaknesses, but it is still early for this game to be decisive in the title race."
Chelsea will again be without John Terry who will sit out the second game of his four-match ban imposed for racially abusing QPR's Anton Ferdinand.
Frank Lampard will also be missing after aggravating the calf injury that forced him out of the Shakhtar clash after just 15 minutes.
"He is going to be out for a few weeks," said Di Matteo. "He's got a calf problem, so we will miss him and it's a big loss for us."