The Premiership pacesetters, who are still 14 points ahead with a game in hand, were reduced to 10 men at the start of the second-half after the harsh dismissal of the midfielder.
McGregor was shown a second yellow card for a challenge on Scott McMann, but Rodgers disagreed with the match official’s reaction.
He said: “It was never a sending-off. It was a really poor decision.
“It wasn’t a tackle. He’s run to try and press the guy who’s thrown the ball and I always ask the players to jump to the thrower. He’s jumped forward, but it wasn’t a tackle.
“They sort of fell into each other. The whole reaction from the ground tells you everything. Everyone was surprised.
“It gave us something else to worry about in the game and the players came through it.
“It gave us a different challenge of how we can cope tactically and I thought they coped very, very well and really controlled the game.”
Rodgers had expressed his dislike of artificial surfaces and on a wet and wild day in Lanarkshire he was happy with the way his side had performed.
He added: “Despite the hurricane, the rain and the plastic pitch, I thought we produced a really professional performance.
“To get three goals here, in what is notoriously a very difficult place, and to play with that composure with 10 men for most of the second half tells you a lot about the players.”
Leigh Griffiths, who is a slight doubt for the midweek game against Ross County, got the opener in the first-half and Stuart Armstrong, with a screamer, and Moussa Demble got the others.