The visitors responded in the first half, as Bristol conceded two goals either side of an Aiden McGeady goal to level the scores.
"I have given big blasting team talks before, as have all managers, but I didn't do that at half time," Coleman told the Sunderland Echo.
"We had a chat, one or two home truths if you like but the second half performance was down to the players. They take responsibility for getting us back into it.
"Responsibility for getting a point. I was delighted with them, they needed to do something, they were rightly booed off at half-time."
Sunderland's next fixture is against Brentford at the Stadium of Light.