After a six-game revival following those damaging back-to-back home defeats by Everton and Newcastle at the beginning of December, United have slumped to three successive defeats.
Another loss to Swansea - who knocked them out of the FA Cup at Old Trafford last Saturday - would represent their worst losing run since 1961.
Giggs is convinced it will not get that bad, but he knows the time to respond is now.
"It is a test of character but I am fully confident we will come through it and we will be okay," said Giggs.
"I have said many times over the years, the defeats and losses generate a bigger feeling than winning things. It sticks with you a lot longer.
"You have to react and you have to try and do something about it.
"It hurts. There are players at this club who only know winning.
"It is important for the older players, who have been through these sticky patches before to help the younger ones."
Giggs was speaking at the launch of a new partnership with Aperol Spritz, who will become the club's official supplier of Global Spirits until 2017.
It is the time of commercial deal upon which so much of United's financial success has been built over the last few years, but could be put at risk should the present malaise continue.
However, Giggs knows it has been a trait of the Red Devils down the years to come out fighting after being backed into a corner.
And the 40-year-old Welshman sees no reason why that trend should not continue.
"That is what we have done in the past and that is what we will try and do at the weekend," he said.
"There are good players in the dressing room who probably haven't been playing to the best of our ability, both individually and as a team.
"If we do that, we win more matches than we lose."
There is a significant difference, though.
For the man who has guided the club through so many troubles, Sir Alex Ferguson, is now consigned to the stands, where he is attracting criticism for piling even more pressure on his successor, who is struggling enough already.
As Giggs was brought onto David Moyes' coaching team to bring some continuity, he is one of those responsible for ensuring the link to the past remains.
And he feels nothing should change.
"At United, we have never got carried away too much when we have been winning trophies and it is also the case that you don't get carried away when you are losing," he said.
"We want to do something about it but we just do the same things as you have done over the years. We go back to basics.
"The manager's job is to prepare the team, as individuals we try and prepare the best way we can."
It is certainly not a time for thinking beyond the next game.
"We are just thinking about doing what we did six weeks ago and trying to get back to the form that allowed us to go on a run of six wins," said Giggs.
"That is what we will need to do if we are to climb back up the table. We need to start winning and winning fast."
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