The Baggies twice took the lead against their opponents, but they were denied the three points by Daley Blind's goal in the final minutes of the match.
Irvine has admitted that while he is upset his team could not hold on and claim the win, there were plenty of positives that he can take from the match.
"I'm disappointed we were so close to getting a fantastic result and for us to be in our dressing room feeling bitterly disappointed is a feeling we won't experience much. We thought the three points were there for the taking," BBC Sport quotes him as saying.
"I felt as though we did use the ball well at times and created opportunities. We scored two fantastic goals with two fantastic moves. They are a great group to work with, Saido [Berahino] has good role models here. He is a good finisher with both feet and is very composed in those situations, I wasn't surprised when he scored.
"I enjoyed tonight and I'm enjoying the job, the players are so responsive. We're making progress and I can't praise them enough for how they've reacted since I came to the club."
West Brom are next in action when they host Crystal Palace in the Premier League on Saturday.