A determined defensive performance saw Colchester hold out for a point.
Bristol City dominated possession but apart from long-range efforts their only clear first-half chance saw Tony Dinning's shot saved by Dean Gerken.
Greg Halford headed over for Colchester and Craig Fagan and Joe Keith also had chances for the visitors.
City piled on the pressure late on but substitute Steve Gillespie wasted their best chance, firing wide in injury time after Leroy Lita's shot was blocked.
Bristol City: Phillips, Smith, Butler, Hill, Bell (Cotterill 89), Murray (Gillespie 77), Orr,
Dinning (Fortune 71), Wilkshire, Lita, Brooker.
Subs Not Used: Amankwaah, Brown.
Colchester: Gerken, Stockley, Baldwin, Brown, Chilvers, Keith, Danns, Watson, Johnson, Halford, Fagan.
Subs Not Used: Izzet, Bowry, White, Garcia, Marriott.
Ref: P Walton (Northamptonshire).