Substitute Dexter Blackstock bagged an 81st minute equaliser to extend Forest's unbeaten start to the season to six Championship matches.
The Reds played for almost 30 minutes with 10 men after the dismissal of Adlene Guedioura and boss O'Driscoll said: "I thought we got out of jail and I said that to Dougie Freedman after the game.
"But we dug in and showed a great deal of resilience and we've got people in the side and on the bench who can score goals.
"Credit to Palace - they have a formidable record on a Tuesday night at home, I think they've only been beaten once in the last two seasons.
"We walk away with a point but we know we can do better."
Guedioura was shown a straight red card after aiming a petulant kick at Palace 'skipper Mile Jedinak.
O'Driscoll added: "In a strange kind of way the sending-off probably gave us the spark that we needed.
"It made Palace a little bit more direct and more predictable and we sort of capitalised on that in a strange way and it's definitely a point won rather than two points lost."
to watch Sean O'Driscoll's post-match interview on Forest Player.