Michael Symes and Adam McGurk scored in the last seven minutes after the hosts had fallen behind to goals from Anton Forrester and William Edjenguele.
"What we've done so far this season is to show that whatever happens in a game, we're capable of handling it," said Rowett.
"I felt it was going to be one of those games where we might find ourselves down a little bit - and I have to say that I thought Bury were excellent.
"They came with bags of energy and did to us what we try to do to teams. At 2-0, you wonder whether you're going to get back into it. But I said at half-time that we'd just got to go out there and show some character like we already have done this season.
"That's the second time we've come from two goals down to get a point already this season and it's important we keep doing that when things don't necessarily go your way.
"The pivotal moment for me was the players who came on, including Michael Symes who was really lively, won his headers and got us a goal when we needed it."