Ange Postecoglou's side went down 3-1 at home against Norwegian champions Bodo/Glimt in their first game of the Europa Conference League knockout round on Thursday.
All is not lost in the tie with the second leg in Norway to come next week but Celtic struggled to reach their recent heights and have little margin for error in the cinch Premiership.
They go into the weekend one point clear of Rangers, who are on a high following their incredible 4-2 win over Borussia Dortmund in Germany.
With Dundee visiting Celtic Park on Sunday, McGregor said: "It's hugely important to bounce back. We're going well in the league. Thursday was a disappointing result. When you have a good result you need to follow it up with another good result.
"This is exactly the same. Everyone will be looking at us to see how we react. Are our heads going to go down? Are we going to work as hard?
"We have to go and answer those questions. The good thing about football is that every three or four days you get a chance to rectify a situation.
"That's exactly what we'll try and do now. Our full focus will be on recovering in the next few days and then we go again here against Dundee."
Celtic had won their previous nine games and 16 out of their last 17 in total so they have the capability of bouncing back quickly.
"These are all huge games," McGregor said. "Especially when you get to this point in the season, every point counts and every game counts.
"You have to be at it. It's up to the players to make sure they rest, get the right fuel into them and go again when the games come around.
"That's the beauty of playing at this club. The standards are always super high and you have to meet them. You've got to do everything you can so when the next game comes, you are fresh and ready to go and you attack every game exactly the same. You need to win."
Dundee have had an unusual week, sacking manager James McPake after two consecutive wins and appointing 64-year-old Mark McGhee for his first league job in four years.
The consequences are hard to judge but McGregor is wary of a fresh approach.
"I've seen this a lot of times in football where teams get a quick bounce off a new manager," the midfielder said.
"Obviously they won their last two games anyway so the players will be feeling good about themselves.
"We just have to do our homework and when we turn up here on Sunday we have to give everything to win the game and that's what we'll be doing."