Edin Dzeko scored his 12th goal of the season to give the home side the lead before former City striker Daniel Sturridge netted his fourth Reds goal in the 30th minute.
Liverpool captain Steven Gerrard scored a sensational long-range strike to edge his side towards three points – but Sergio Aguero rescued a draw for his side with a cunning finish.
With United winning 1-0 at Fulham on Saturday, the Citizens are now nine points adrift of their derby rivals, yet Mancini is convinced that City can still catch them.
“No [title race is not over]. Seven or nine points don’t change, I think we can recover it,” he told BBC Sport.
Mancini criticised Daniel Agger’s challenge in the lead-up to Sturridge’s goal, with referee Anthony Taylor signalling no foul before the striker equalised.
With Kompany already sent off for a similar tackle against Arsenal in January, the City manager was unsurprisingly aggrieved by the referee’s decision.
He said: “Before their first goal there was a big fault, if it happened against us it would be a red card but instead the referee didn’t see anything. But in the end I feel that was the right result.
The City boss also praised Aguero for his ingenious leveller which denied Liverpool a rare win at the Etihad.
“Few players can score the kind of goal that Sergio Aguero scored, but I feel he and Edin Dzeko should have played better tonight. We didn’t play well.
“In the last month we played well in all the games but we were so nervous in this game and I don’t know why.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news