Sam Allardyce was unhappy with his Bolton side's performance. He said: “We were not good enough in the second half and laid down too easily.
“Our big players did not play today and, with our injuries, it proved a bridge to far.”
City manager Kevin Keegan was pleased with his side's display on a wet and slippery surface.
Keegan, an advocate of attacking football, was particularly pleased with his side's defensive display praising centre-backs Richard Dunne, Steve Howey and Sylvain Distin.
“We limited an inventive Bolton side to hardly any chances and I see those three as a rock to build the side on,” enthused Keegan.
City took the lead midway through the opening half when Howey, back after a three-match injury lay-off, found the net for the first time this season.
Kevin Horlock flicked on Eyal Berkovic's corner leaving Howey with a free header from four yards.
City sealed victory 11 minutes into the second period when Berkovic scored his first League goal of the campaign.
Striker Nicolas Anelka, a threat throughout, turned provider with a great threaded throughball to release the Israeli, who slotted home a low shot.
City's defence was rarely threatened, though goalkeeper Peter Schmeichel made an excellent save in the first half to deny Henrik Pedersen and then late on a fine double stop to thwart Jermaine Johnson and Jay-Jay Okocha.