With 70 minutes on the clock Jonny Hayes was flagged offside after running on to Niall McGinn's pass and then cooly finding the back of the net.
And McInnes said: "There's been an honest mistake by the official.
"I felt at the time he was onside and I've watched it again now a few times and it's clear he was played onside.
"It's frustrating, I thought we had enough good chances, certainly in the second half, to win the game.
"I thought we were better than St Mirren but I'm still looking for improvement.
"It was a frustrating day for us. If we get ourselves in front then I think we win the game comfortably because I never at any point felt too troubled by the opposition. It's two points dropped."