Rodgers' Celtic side ran out 1-0 winners in the encounter at Celtic Park on Sunday thanks to Olivier Ntcham's second-half goal.
And, while the ex-Liverpool manager was delighted with his side's performance, he believes Gerrard is already moulding his side in his own image.
"Steven has done a great job going into there, he's got the team organised and they are threat, but I thought today we were excellent. I think the trademark in these games is our calmness," he told reporters after the game.
Nevertheless, Rodgers believes that Celtic could have won the game by more than a single goal, having dominated the majority of the game.
"It was a very, very good performance. Maybe the scoreline makes it look a bit tighter but I thought we were the really dominant team," he added.
"Defensively we pressed the game really well and then with the ball moved it well and had good positions on the pitch. We've hit the bar four times and Alan McGregor made some outstanding saves."
Celtic captain Scott Brown agreed with his manager's words, even going as far to say that he and his team-mates were well on top.
"I think the performance was exceptional. From start to finish we dictated, they came to Celtic Park and we showed them who was boss," he added. "It was all about possession and keeping the team spirit going.
"The lads have been outstanding this year and the last two seasons so it's about kicking on from here. They didn't want to press us too high up the park because they had a hard game on Thursday so they were probably a bit leggy.
"We showed our qualities yet again today. We don't listen to press. We know what happens in that dressing room and we have a great spirit and we showed that on the park.
"We celebrated together and win together and lose together. It's about maintaining this league, that's why we have done so well over the few years."