Mark Hughes took the opportunity to rest a number of key players with qualification already secured before kick-off.
Kasper Schmeichel, Tal Ben Haim, Javier Garrido, Gelson Fernandes and Ched Evans all came into the starting line-up, while there was a surprise inclusion for record transfer buy Robinho up front.
City were looking to continue their impressive away record in Europe which had brought six wins from their last seven games, but Racing had more urgency in the early stages as they sought the win which they required to reach the knockout stages.
It was little surprise when the home side took the lead in the 18th minute as Oscar Serrano reached the byline and Pereira Rodriguez Jonathan slotted home the loose ball after Schmeichel could only divert the cut-back to the feet of the waiting striker.
Serrano then turned goalscorer on the half-hour mark as he played a neat one-two with Jonathan to open up the City defence before finding the bottom corner with a composed finish.
Robinho was replaced by Stephen Ireland at half-time and the 1,000 travelling City fans had little to cheer during a below-par second period which was punctuated by niggly fouls.
Racing made it 3-0 in the 55th minute as a Pedro Munitis cross was not cut out and Juan Valera was in the right place to score from close range after Ivan Sierra Marcano had flicked the ball on.
Vincent Kompany came on for the ineffective Elano in the 61st minute, but City should have fallen further behind five minutes later when Mohammed Tchite missed an open goal with Schmeichel in no man's land.
The visitors did pull a goal back in stoppage time when Felipe Caicedo scored a late consolation after heading in a cross from Pablo Zabaleta.
But despite their impressive victory, Racing were left to rue what might have been as a late fourth goal for Paris St Germain in their rout of FC Twente sent the French side and not themselves through in third place.