The Robins head coach saw his side rescue a share of the spoils thanks to Sam Baldock's 74th-minute equaliser, but City are now without a win in the Football League since March - a run stretching back 19 games.
Colchester grabbed the lead after half an hour through Matt Taylor's powerful header from a Luke Garbutt cross, but the U's themselves have now not won for seven matches.
While Ashton Gate fans are becoming increasingly restive, O'Driscoll insists there is no shortage of commitment from his players.
"I thought we dominated both halves," said O'Driscoll.
"When Marlon Harewood went on as a substitute we took a gamble with three strikers. When you press for a win you can get caught and we left the back door open for Colchester to have a late chance to take the points. Thankfully we were able to recover.
"A couple of our young players found it hard after the midweek League Cup tie at Southampton, but they will learn that by looking after themselves and getting stronger they will be able to handle three games in a week.
"The longer the run without a league win goes on the greater the pressure, but I thought the players coped with it well and there was certainly no shortage of effort."