The Baggies conceded twice during the opening 45 minutes at The Hawthorns on Saturday as Palace took control of the game, but goals from Victor Anichebe and Saido Berahino after the break earned them a share of the spoils.
"I am disappointed because it wasn't us for 32 minutes. At half time I was the most angry I have been," Irvine is quoted as saying by BBC Sport.
"We gave ourselves a mountain to climb, but credit to the players for keeping going to the end and I think we got what we deserved. I was pleased to get a point, having left ourselves a lot to do."
The result has seen West Brom move up to 12th place in the Premier League table after nine matches.