The visitors had a wonderful chance to clinch all three points four minutes from time when skipper Matt Tootle fired wide from eight yards after good work from Mathias Pogba.
It could prove a costly miss. With nothing to play for, City created little, although substitute Martin Paterson might have done better when shooting wide from Wade Elliott's 76th-minute pass.
Crewe created the best chances of a competitive first half, Pogba producing an air-shot in the sixth minute when well placed to score.
The striker also headed wide in the 28th minute and had a shot on the turn blocked on the line in a crowded goalmouth.
City's best first-half effort was a close-range back-heel from Jay Emmanuel-Thomas, which struck a defender.
Crewe built a succession of promising moves, but lacked a killer punch in front of goal. Their final game is at home to Preston.