McInnes reckoned the Dons should have been awarded a penalty for a handball on the line by Dylan McGowan, which would have resulted in a red card with the hosts leading 1-0.
Aberdeen were given a spot-kick moments later for another handball, but goalscorer Niall McGinn was denied a brace when Jamie MacDonald saved.
McInnes said: "I think there should have been a penalty and a red card for Dylan McGowan for handball on the line. The ball's travelled at a fair speed but it's travelled 5 or 6 yards and it's a clear handball.
"Between the officials, they should see that. It's too big a decision to miss. That was pivotal in the outcome of the game.
"The missed penalty was a chance to get the second goal which was the least we merited. It was a total domination in the first half."
Aberdeen were reduced to 10 men when Barry Robson picked up a two yellow cards when he tangled with Jason Holt, and McInnes claimed the midfielder was unlucky with the second caution.
"I accept he's ahead of the wall so you could say encroachment is a yellow card by the letter of the law. The second booking, I think he's actually tried to get away from the challenge," McInnes added.
Hearts counterpart Gary Locke felt his side showed their mettle in the Granite City after losing at home to St Johnstone last week.
"The team spirit has been fantastic this year, and last week was the first time we'd been disappointed in how we'd performed," Locke said.
"The boys have come back in the right manner this week, and the effort the players gave was fantastic and I'm delighted to get the result our efforts deserved.
"It's a young team, but if they put the work-rate in as they did today, they'll give themselves a chance."