Liverpool were rewarded for a bright start when they took the lead in the 34th minute, with Martin Skrtel emphatically heading Steven Gerrard’s corner past Joe Hart.
However, Rodgers’ side were pegged back when confusion between Pepe Reina and Martin Kelly allowed Yaya Touré to momentarily equalise with 27 minutes remaining.
Luis Suárez appeared to have rescued three points for Liverpool when he netted a superb free-kick, but Skrtel’s sloppy back pass was intercepted by Carlos Tévez, and the Argetina forward rounded Reina to level in the 81st minute.
“Sometimes the best team can’t always win but if you don’t win it’s important you don’t lose,” Rodgers told BBC Sport.
“You can’t win every game, that’s why there’s only one champion. I thank the fans, it was a wonderful atmosphere they created. We will have more days like that but get the win.”
City manager Roberto Mancini was pleased to take a point after a difficult test at Anfield, but the 47-year-old was keen to emphasise the English champions are still not at their best.
“I think that a draw is a correct result. We didn’t deserve to lose because in the first 30 minutes we played well and we had chances to score,” said Mancini.
“We are not 100 per cent for many reasons, it is important we didn’t lose this game. We got a gift from Liverpool, the second goal was a gift.”
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