Steven Gerrard converted a first half penalty after Stefan Savic had fouled Daniel Agger, which proved to be the only goal of the game.
City were poor in the first half, and only a handful of excellent saves from goalkeeper Joe Hart prevented the Merseysiders from going into the interval with more of an advantage.
Although the hosts did improve in the second half they could not beat Pepe Reina in the Liverpool goal, and Kenny Dalglish’s men left Manchester with a win.
Despite the defeat and poor performance by his team, Roberto Mancini feels that his side will recover and get back to the ominous form that lit up the Premier League before Christmas.
“I thought we played better in the second half, we were poor in the first half. In the end we didn’t deserve to lose, but we were unlucky,” he told Sky Sports.
“This moment is very difficult, but it is important that we stay very confident. This moment is not a good moment. We have to continue to work and continue to believe in ourselves.
“We were without three or four players, but in the second half we played well. We did well until three or four days ago, now we have lost two important games.
“We can win away against Liverpool. It will be difficult, but we will try. It is only one goal,” he concluded.
City take on Wigan at the DW Stadium next on Monday night, whilst Liverpool entertain Stoke on Saturday.
By Gareth McKnight