The Hoops were beaten 5-0 at home by the star-studded French team in their Champions League opener on Tuesday night.
But they returned to top form in their Ladbrokes Premiership encounter against the Staggies, with midfielder Tom Rogic driving them ahead in the 13th minute.
Three minutes from the break the 21-year-old French striker Moussa Dembele, back for the first time since July after recovering from a hamstring injury, fired in his first goal of the season.
Winger James Forrest added two more in the second half to extend the treble winners’ unbeaten domestic run to 55 games.
“It was perfect,” said Rodgers. “The players deserve a huge amount of credit.
“I said to the players, ‘We take our medicine, we learn from it’, and this is what this group is very good at doing.
“We remain very positive, press the reset button and we go again.
“They were excellent in training on Thursday and Friday. We tried something different today in the shape of the team and I thought as the game went on we got better and better.
“It was a mark of a good side that you can respond, score four goals and keep a clean sheet. It was a really good performance.”
Celtic moved two points clear of second-placed Aberdeen and five clear of traditional rivals Rangers ahead of the Old Firm clash at Ibrox next week. They also have a Betfred Cup tie against Dundee at Dens Park on Wednesday.
Rodgers was pleased to see Dembele back and scoring but will remain cautious ahead of a busy week.
The former Swansea and Liverpool boss said: “It is great for his confidence and it was a very good finish. We will see what his reaction is. We don’t really need to force him again.
“We have a really good squad of players, young Odsonne Edouard, Leigh Griffiths... we have other players who can play there.
“That is the reason for bringing in the third striker (Edouard). Leigh and Moussa have had injury history so we don’t want to push it.”
Staggies boss Jim McIntyre described as “incredible” Celtic goallkeeper Craig Gordon’s second save in a double block from substitute Craig Curran and Davis Keillor-Dunn, when the score was 2-0.
He said: “It was fantastic, especially the second part of it. It was an incredible save, but he is a top keeper.
“The sign of a top keeper is when you don’t have a lot to do and then you have to produce when it matters and he certainly did that.
“We had a good chance before their third goal when Michael Gardyne has a shot but we have three-on-one at the back area.
“All of a sudden they counter-attack and we are done and it is 3-0 rather than a good chance to make it 2-1. These are the key moments when you come to places like this.”