There was disappointment for Liverpool who must be kicking themselves for failing to take maximum points and make up ground on the three teams above them in the table.
They created 17 scoring chances to City's two, but just could not find a way to goal through a combination of fine goalkeeping from Joe Hart and poor finishing.
As for City, they remain in with a shout of fourth place and are still unbeaten in the league at Eastlands, although this was the first time this season that they have failed to score at home in the Premiership.
Liverpool made five changes from their last-gasp Boxing Day win at Derby as they fielded their strongest line-up.
Fernando Torres and Dirk Kuyt played up front with Yossi Benayoun and Harry Kewell out wide in an attacking formation.
City recalled former Liverpool player Didi Hamann and Elano after the pair had been rested for Thursday's home game against Blackburn Rovers.
In a desperately poor opening half, Liverpool had marginally the better of the few clear-cut chances.
Left back Fabio Aurelio was, surprisingly, their most potent attacking threat, twice going close with spectacular long-range shots, the second being brilliantly tipped over by Hart who had earlier denied Kewell.
City mustered only one meaningful opening, the first chance of the match, when Darius Vassell beat keeper Jose Reina to a high ball but headed narrowly wide.
Liverpool made a far more purposeful start to the second half carving out a number of gilt-edged scoring chances.
Torres had two great openings within the space of 60 seconds, the second rolling inches wide after he had poked the ball past Hart.
Steven Gerrard crashed a free-kick narrowly wide, while a terrific shot on the run from Benayoun was tipped over the bar by Hart.
City weathered Liverpool's early onslaught, but failed to cause their opponents any trouble defensively as Reina remained a spectator for much of the afternoon.
City manager Sven-Goran Eriksson sent on Rolando Bianchi, Geovanni and Gelson Fernandes in a bid to break the deadlock while Liverpool threw on Ryan Babel in an attempt to provide more attacking ideas.
The changes were to no avail as neither side could conjure the goal which would have broken the deadlock.
Liverpool came closest late in the game when Kuyt's header was brilliantly saved by Hart with Richard Dunne completing a goal-line clearance as City preserved their clean sheet.