Bolton went in front inside two minutes when Darren Pratley's cross from the left was allowed to pass across the six-yard box and Liam Fontaine deflected it into his own goal.
But City were in no mood to surrender and equalised four minutes after the break when the unmarked Steve Davies headed home from an Albert Adomah cross.
Craig Davies won it for Wanderers with a 79th-minute penalty, and O'Driscoll said: "Our performance had everything I would want apart from enough goals to win the game.
"I was disappointed we didn't get a penalty for handball late in the game, but that's the way things have been going for us.
"We have a big summer ahead with a number of contracts up, but I can't ask more in terms of effort than the players showed here.
"The fans have stuck with us, but we have known for a while that a change of strategy was necessary at the club.
"We can't keep on throwing millions of pounds at trying to achieve success. It hasn't worked."
- Sports & Recreation
- Darren Pratley
- Liam Fontaine
- Craig Davies