United suffered their first defeat since the beginning of January when they lost 1-0 at Wigan on Wednesday night, allowing City to cut their lead to five points with five games of the season remaining. Giggs has made it clear he wants Aston Villa this Sunday and Everton the following week to be disposed of with the minimum of fuss.
He said: "It is important that we get six points from the next two games. We are at Old Trafford, we are at home. We will be looking to win both games and put the pressure on. We have had poor performances throughout the season and results but we have always bounced back."
Unlike the previous two shock defeats, there did seem to be an element of the law of averages catching up with United at Wigan.
After all, manager Sir Alex Ferguson always knew his side could not continue to win every game and, after eight straight triumphs, were due a dip in fortunes.
In addition, Wigan, having lost all previous 14 matches against United, had to come out on top at some point and were in decent form, beating Liverpool away and only leaving Stamford Bridge with nothing on Saturday due to the incompetence of the match officials.
Giggs has been around long enough to accept unexpected setbacks are part of the overall test of champions, which is why the veteran Welshman is urging his team-mates to keep their chins up.
"We don't have to get too down," he said. "It has happened quite a bit this season where there has been the odd display where we just haven't performed.
"The main thing is that we have recovered from it. That is what we have to do again."