Bradley Wright-Phillips and Matthew Mills both went close before Ishmael Miller gave City a deserved lead after 25 minutes.
Danny O'Donnell pulled the City striker down in the box and Miller stepped up to drill the ball low past Martin.
City then doubled their lead five minutes before the break through Sun Jihai, who had taken the ball around Martin after a fine one-two with Kelvin Etuhu.
Liverpool's ex-United man Ramon Calliste tested Nicky Weaver just after the restart and late on Idrizaj hit the bar with a header but City held on comfortably for the three points.
The Blues finished the season with 15 wins, 8 draws and 5 defeats, 3 points behind second-placed Villa and 6 behind league winners United.