Second-half goals from Jay Emmanuel-Thomas and Scott Wagstaff sent City into the third round following a 2-1 win over Palace at Ashton Gate.
For O'Driscoll's young team it was just their second win in 14 games and their first on home soil this season.
The Robins head coach had plenty to be encouraged by in a fine display but admits the intensity of their start to the campaign is really stretching his squad.
"It was a night of positives, we've saved our best performances for this cup," he said. "Gillingham away was probably our most fluid performance and this was on a par with that.
"You want your cup form to have an influence in terms of confidence.
"We don't want the cup form to hinder the league form and we've lost two players, 19 and 20, through fatigue tonight as they aren't used to playing Saturday and then Tuesday in games of this intensity.
"We are skating on thin ice with the squad I think. They changed all 11 players, we are not able to do that.
"The depth of the squad needs to be addressed because we are worried the team that goes out at Gillingham on Saturday will be less balanced than we were here."