A late effort from Bryan Oviedo bagged Everton their first win at the Theatre of Dreams in 21 years - leaving United languishing in ninth place and 12 points behind Premier League leaders Arsenal.
The 40-year-old Giggs, who has won the title 13 times with the Red Devils, said: "We have to pick ourselves up.
"We can't feel sorry for ourselves for too long. We have a home game against Newcastle on Saturday and hopefully we will get a different result.
"We were on a pretty good run. We just have to get over this disappointment now and get on another.
"The gap is bridgeable," added the Welshman.
"Hopefully we can start picking up points again but we will get a better idea come the new year. We have had a few disappointing results over the last couple of weeks.
"The performances haven't been that bad. Maybe we are just not getting the rub of the green or taking our chances when we should.
"It is the story of a few games this season. When we have been on top we have not taken our chances.
"If you do that in this league you are going to get punished."
I agree United are where there should be, because the reults don't lie. But what has changed from last year to now? Well, the obvious is the management and Moyes is not the man for the job now, and I didn't think he was when he was appointed either, I'm not jumping ship, I was never on board because he's trash. The other reason: teams invested and strengthened their squads. Teams are always getting better and if you're not getting better, you will be left behind such as we have been this year. @nugget, I dont give two sh*ts what Giggs did in one game against Real Madrid last year, how many games since then has he been a ghost, been beat by his man, been out of position? That's not enough to justify him holding out from retiring just so he can have a run about and keep someone more qualified on the bench. I'm not taking away what he's done, but his time has passed. Now he's just being selfish. I see often times if the ball is played into space, he won't get it, it must be passed directly to him and when its not, he flails his geriatric arms in the air like it was the other person's fault.- reddvl7