Lewis McGugan gave The Reds the lead with an outstanding long-range strike before Chris Eagles pegged them back despite shouts for a foul.
And just after the break Greg Halford was punished for dallying in possession when Kevin Davies set up Marvin Sordell to put The Whites in front.
Despite the home side’s early second half pressure, Forest responded through Andy Reid. The Irishman finished brilliantly after good work by Dexter Blackstock and Simon Cox.
O’Driscoll said: “It was like a 5-a-side game with 22 players. If you were a neutral I’d imagine you’ll have been enthralled at times.
“We got an unbelievable goal from Lewis and I don’t know whether we got complacent or Bolton upped the ante but we ended up hanging on until half time really.
“From there I decided there was no point in trying to hang on and thought ‘if we’re going to get beaten we might as well go down trying to do the things that we want to do’. Credit to the players, they took every opportunity to try and pass the ball and we took a point.”
“This is the first time we’ve come back from being a goal behind so it was a good test of how the players would react. Credit to them, they did so in a positive manner and deservedly got the equaliser.”