Ryan Stevenson headed the Jambos into the lead only for the home side to earn a share of the spoils when Jamie Hamill put through his own net.
"I'm delighted with so much of the performance. The critical part of it comes from passing up so many opportunities," said McInnes.
"I thought Jamie MacDonald pulled off a lot of saves, and good saves at that, but a lot of the opportunities we had were at a good height for him.
"I couldn't ask for much more from the players. It was difficult for the likes of Gavin Rae and Isaac Osbourne who are moving on.
"You would never have known it from the way they played. They were determined and put in a good performance.
"I was delighted with the response to falling behind. It would have been easy to say it wasn't going to be our day and feel sorry for ourselves.
"It certainly didn't feel like an end of season game. Both sets of supporters were excellent.
"There was good solidarity from the Hearts support but there was a big support from Aberdeen getting behind the team, and I think they recognised the effort the lads put in."