Glenn Murray and Stephen Dobbie scored in either half to put Palace in charge and City are now rock-bottom of the Championship, although they pulled a goal back late on when Palace's Jonathan Parr headed the ball into his own net.
But O'Driscoll said: "We have just played Cardiff and Palace away, two of the most difficult games you will get.
"We got beaten by a piece of quick thinking or sloppy play by us, whatever way you want to look at it, but we competed and tried to stop them doing what they did to Middlesbrough (a 4-1 win for Palace on Saturday).
"We were brave and pressed high up the pitch. We gave it our best and I would have taken the performance all day long.
"Nothing fazed us and we kept going. If you have a group of payers prepared to do that, then that is gold-dust.
"The worst case scenario is getting beaten twice, thumped, the spirit broken and the attitude not right but we are a million miles away from that.
"We are disappointed with the result, but happy with the attitude. The enthusiasm to play the game and work hard for each other was there."