Ross Barkley had Villa ahead on 76 minutes, with Evanilson scoring in injury-time an equaliser.
Iraola later said: "It is always nice when you have a point at the end in the last minute of the game. I don't feel we played well but we competed well. We faced a very good team and they started better than us. It was difficult.
"I don't want to talk about the referees. I prefer not to speak. After I was suspended I prefer to start a clean slate."
On the equaliser being from a well-worked set-piece, he said: "Especially with the keeper, everything we were putting on the second post he was claiming everything. Luckily the last one it is difficult header but it was a great goal in a great moment."
On Mark Travers' performance for Bournemouth, Iraola added: "He made very good saves and kept us in the game when we were suffering. Everyone has stepped up and we finished much better.
"We played better against Arsenal but today we showed more character. You feel intimidation here and it is tough to survive but we kept in and got the draw."