The visitors were fortunate to come away with a point in a mistake-riddled performance at the AESSEAL New York Stadium as Bruce admitted the Owls had “got away with one”.
He said: “You can’t fault their attitude really, staying in it and getting something late on.
“We’ve made more mistakes today than we probably have done in the previous three weeks that we’ve been here.
“We’ve gifted Rotherham the first goal and the second really, and that’s been a bit unlike us.
“We are not satisfied certainly and the manner in which we have played however I am delighted that we have got something out of it which shows a little bit of attitude anyway.
“We’ve got to stop making those mistakes like we did today because we’ve nearly given Rotherham the win.”
Wednesday goalscorer Fernando Forestieri was sent off for his part in the celebrations after Iorfa’s equaliser after receiving a second yellow card.
But Bruce was pleased with the late goal, despite the performance: “There’s nothing quite like scoring late on and we’re delighted with that.
“Look, we’ve got away with one, I’m not disguising that. I’m not going to b******t you, we got away with one because we made too many mistakes.
“We got sucked into the way Rotherham play, we put it forward far too early.
“Just ask the goalkeeper he’ll lump it up the pitch and it’s not the way forward for us, it’s certainly not the way we want to play but we got sucked into it.
“It’s very difficult here because they do ask you the question.”
Wednesday’s run of clean sheets came to an end with the result against the Millers, but have now drawn three games in a row.
The Owls play Swansea City at Hillsborough in next weekend’s Championship match.