Table-toppers Liverpool moved seven points clear of Manuel Pellegrini's men - who still have two games in hand - courtesy of Philippe Coutinho's 78th-minute winner in Sunday's 3-2 triumph.
That strike came after the hosts had surrendered the two-goal advantage handed to them by Raheem Sterling and Martin Skrtel's first-half goals.
And Coutinho's late effort capped a remarkable game at Anfield on a day that could prove decisive in the top-flight title race.
"Ten (consecutive) wins now in the Barclays Premier League is an incredible achievement and, against all the odds, we are where we are and still fighting," Liverpool manager Rodgers, who saw Jordan Henderson dismissed late on, said.
"It was a wonderful game of football. I think it had everything.
"The performance of the players today was sensational. To dominate like we did in the first half, to play with that energy and intelligence was remarkable."
David Silva turned the game on its head after the interval, reducing the deficit and then seeing his shot deflect off Glen Johnson and Liverpool goalkeeper Simon Mignolet to tie the scores.
Rodgers was not surprised by City's resilience and revealed that a tactical switch shifted the momentum back in the hosts' favour - culminating in Coutinho's goal.
"Second half you expect City to come back, they've got wonderful quality, they're a great team, the manager's a great manager," he added.
"They get back into it with the first goal...then we were unfortunate to concede the second goal - it's an own goal - and of course it gets to 2-2.
"I felt then they started to have a wee bit of energy and bit of joy down the side, so we changed from the diamond to the 4-3-3 to open the game up a bit but also to protect the sides whenever we were defending.
"That allowed us to get some control back into the game, (and) we end up getting the winning goal with a great finish."
Liverpool's next Premier League assignment sees them visit Norwich City on Saturday.
