A 78th-minute winner from Philippe Coutinho gave Liverpool the points from an enthralling clash at Anfield after a David Silva strike and a Glen Johnson own goal had dragged City level following early goals from Raheem Sterling and Martin Skrtel.
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"We didn't start well in the match and they were better than us until they scored the first ," he told the Manchester Evening News.
"Then there were a lot of set-pieces, and that is how they got the second goal, from a corner kick.
"After that there was not a lot of continuity in the match, but in the last part of the first half we played much better than them but couldn't score.
"We started very well in the second half and got the two goals - after that Silva could have scored a third and we would have been in front, but they scored from our mistake.
"Given that we were better than them for more than 45 minutes, maybe 2-2 would have been a fair result.
"We're obviously not happy about the result but we know we have matches ahead and you have seen in football that we can still win - they can still make mistakes.
"Hopefully we will win the rest and expect some mistakes from Liverpool. No-one left the stadium feeling they were champions, and we have plenty of matches."