The Second City derby saw both sides muster 28 shots between them but the spoils ended up shared with neither team able to break the deadlock at St Andrew's.
"I think we were better when we made the changes," Bruce told Sky Sports News. "Physically, it was important we stood up to the barrage they had, then the longer the game goes on you're hoping you can produce a bit of quality at the top end of the pitch.
"We've had a really big, big chance in the game, and they did as well just after half time, but you're hoping you can take that and come away with the win, which is always nicer than a draw.
"It's never easy [at St Andrew's]. It's a big hostile derby and the supporters were bang up for it again. So we're delighted we haven't been beaten but maybe disappointed that we could have snatched it. Overall, though, I'm delighted that we've stood up to the big physical challenge that Birmingham threw at us."
Villa remain sixth in the Championship table following the derby draw.