Hayes was flagged offside after running on to Niall McGinn's pass and slotting home in the 69th minute.
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."
McInnes stretched his unbeaten run to four games since he took over from Craig Brown but had other chances to take three points.
Scott Vernon saw a close-range header blocked on the line by Marc McAusland and Ryan Jack volleyed against the outside of a post.
"It was a frustrating day for us," McInnes said. "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."
- Sports & Recreation