The Baggies beat their local rivals 1-0 at The Hawthorns thanks to Craig Gardner's first goal for the club.
"Relief is one of the emotions," Irvine said, with Albion up to 14th on Saturday. "Obviously I'm delighted first of all. We probably deserved to win some of the other games recently.
"We're always looking for more, but I felt as long as we made the right decisions and kept patient the chances would come.
"I thought the crowd were fantastic and it didn't surprise me to be honest. I've not been involved in this derby before, but I've been involved in enough to know the place would be bouncing. The fans were great and right behind us all the way, but like the rest of us they got anxious towards end."