Forest looked to be heading towards a second successive pre-season win as they lead 2-0 at half-time at Meadow Lane, thanks to a David McGoldrick goal and a Lewis McGugan penalty.
But Notts came storming back after the break and goals from Alan Judge and Yoann Arquin forced a 2-2 draw.
Boss O'Driscoll told Forest Player: "Pre-season friendlies can fill you either with a false sense of security or a sense of paranoia and I think we saw that in the first half, when we believed we were okay.
"But we were conscious of playing our back four - which is not strong enough yet - in too many games. We have a game on Friday and a game on Monday to come. We could have done without one of these games, to be honest.
"We cobbled together a back four in the second half and it made a difference but the attitude was first class and we will take one or two positives out of it.
"It is blatantly obvious that there are still gaps in the squad. My right back was a central midfield player, another central midfield player was in the centre of defence and we drafted one of the young lads in at left back.
"On top of that we had an 18 year old, who is not the most experienced, who we were asking to lead the back line. That was always going to prove difficult and they exploited that lack of knowledge and experience.
"But they will learn from the experience. They have to. There is no point in playing pre-season games if you are not going to learn from them. We will take the positives out of this."