The unexpected defeat at the Reebok Stadium, coupled with Arsenal's continuing good form, means United head into Monday's clash with Fulham five points adrift of the Gunners.
Although the season has not yet reached its midway point, Sir Alex Ferguson's men are aware there is no room for further failure - at least until December 16 when United square up to Liverpool at Anfield on the same day as Arsenal host Chelsea in what is already being billed as 'blockbuster Sunday'.
But Giggs revealed there has been no tension in the Red Devils camp, just a clear-headed analysis of what went wrong at Bolton - and the usual steely determination to put it right.
"Outside the club, a lot is made of it when we lose a game," he said.
"But inside there are no alarm bells.
"You have to be realistic - everyone is going to lose occasionally. One game is nothing. It is when you lose two or three on the bounce that you should really start worrying."
Although it is not totally unheard of for Fulham to win at Old Trafford - they last managed it in 2003 - United have triumphed in their last five meetings. With Wayne Rooney set to return, they are strong favourites to extend that sequence to six.
With no internationals to disrupt the fixture list until February and top spot in their Champions League group confirmed already, the Red Devils effectively have a two-month run in which to flex their title muscles.
It is a time of the year when United have traditionally been at their strongest - and Giggs, veteran of all previous nine championship triumphs under Ferguson, is hoping history repeats itself.
"This is a time of year when we have won a lot of games in the past," he recalls.
"The last international break was not too good for us - because we were brilliant against Blackburn before it and definitely were not against Bolton immediately afterwards.
"Like any team, if we are in good form, we want the games to come thick and fast.
"We hope we can get our form going into the Christmas period again, because there are four or five games within 10 or 11 days - with a lot of points to be won. We don't want to be dropping any."
Giggs is among a clutch of players expecting a recall after starting last Tuesday's win over Sporting Lisbon on the bench.
Carlos Tevez, Wes Brown and Owen Hargreaves are in the same situation - while Rooney has stepped up his training in recent days after recovering from an ankle injury, leaving Ferguson confident the England forward will end a three-match absence.
Apart from scoring 10 goals in 10 matches for club and country immediately before the freak training-ground injury which left him on crutches, Rooney has also gelled with Tevez.
For a creative player such as Giggs, having both men available is a major plus.
"Wayne and Carlos have struck up a really good partnership - so with Wayne coming back and Louis Saha fit again, the manager has a lot of options," said Giggs.
"It is great to have Wayne back. Before he got injured, he was on an excellent run of form. He is a quality player and he is always a threat.
"The key for us is to perform to our highest level; if teams come to Old Trafford and we are not at our best, it only encourages them.
"If we are playing at our best, playing at a high tempo, as Manchester United can, we will cause teams problems and get the games won. It is as simple as that."
