It was the 10th consecutive victory the Glasgow club had recorded over their north-east rivals and came after both teams were reduced to 10 men with the red carding of Mikael Lustig and Sam Cosgrove respectively in the second-half.
Rodgers, whose team had been knocked out of the Europa League by Zenit St Petersburg in Russia on Thursday night, was delighted with his side’s performance and the final outcome of the match.
“I thought it was a brilliant win for ourselves,” he said. “It came 72 hours after we had come back from Russia. It is a tough place to come for an away game so soon after that. But I thought we dealt with everything really, really well.
“In the first half we had control of the game. In the second half we slowed the game down and played at a different tempo. We had to deal with the longer ball. I understand why Derek (Aberdeen manager McInnes) would have to do that on the pitch. It was difficult to play on. But we coped with that really well.
“We showed real resilience and good mentality when we went down to 10 men. To manage the game in that situation and score a brilliant counter attacking goal was pleasing. All in all, I am really proud of the players today.
“It was always going to be a really tough game. It was another signpost towards where we want to go and a fantastic win for us.”
Rodgers singled out Scott Brown, the Celtic skipper, for special praise for how he had withstood the rough treatment dealt out to him by the Aberdeen players, and criticised the challenge which had led to Cosgrove being red carded.
“Scott is a big game player, especially in those difficult moments,” he said. “When it goes to 10 men he revels in it even more Browny is a brilliant leader. It was a naughty challenge on him from the boy who got sent off. But he takes it, shrugs it off and gets back up again to dominate the game. He’s a big game player and showed it again today.”
Meanwhile, Rodgers has stressed that he is keen to keep Tom Rogic, who is reported to have turned down the offer of a new contract, at Celtic and is hopeful the Australian midfielder will agree to sign an extension to his current contract.
“It will always be between the club and the players’ representatives, but he’s got a year and a half left here,” he said. “He’s been brilliant in my time here and we want to keep him. It will be ongoing with him and his representatives.”
Meanwhile, McInnes, whose side fell three points behind second-placed Rangers as a result of the loss, insisted Aberdeen had made progress during his time in charge despite the 10 consecutive defeats they have suffered against Celtic.
“It’s not a stat we are proud of but it’s a stat that was common for a while,” he said. “We have beat Celtic previously in my time here, but we haven’t been able to beat the current Celtic team for the last couple of seasons.
“Ultimately we are now judged and looked at on our results against Celtic. But there was a time here when we couldn’t get a result against Inverness and Ross County so there has been a lot of progress here.”