The Dons conceded inside the first minute when Henri Anier netted his second goal for the Steelmen but managed to fight back through a pair of penalties from Niall McGinn and one goal from Mark Reynolds.
McInnes felt his side were a bit unlucky to go behind so early but was delighted with how they responded to grab their second win of the season.
"But I thought our response was excellent. Even at half-time, we could easily have felt sorry for ourselves, in the fact we passed up a couple of opportunities and hit the bar twice.
"They got their just rewards. It was a good strong performance with the right level of mentality.
"They don't need to show me we have good players, I know I have good players, it's the other side we will need to show.
"We will need to come from behind again and at no point did I feel we were ever going to give up the ghost. It was an immediate response and there was some real good play in the first half."