West Brom were staring down the barrel of defeat after Brede Hangeland poked home from an early Palace set-piece, before Mile Jedinak scored a second from the spot in first-half stoppage time.
However, Anichebe entered the fray for the second half at The Hawthorns and made a quick impact with a close-range header from Chris Brunt's corner, before drawing the penalty from Jedinak's reckless challenge from which Saido Berahino levelled in injury time.
Irvine was disappointed with his side's sloppy start, but stated he had a feeling that Anichebe may have a crucial role in the Premier League clash.
"I was bitterly disappointed with the first 32 minutes of the game. From that point we followed the game plan - alright, we lost the penalty on a counter-attack, but for the first 32 minutes we were awful," he said.
"After that we did what we were supposed to do and followed the game plan and we got our rewards.
"There's no doubt he [Anichebe] made a difference and I thought before the game that we might need him.
"Having watched Palace and looked at their strengths and the way they're able to play then I felt as if Victor would be needed at some point during the game.
"Unfortunately he wasn't quite ready to start the game but it was important he was fresh enough to make an impact if we needed him. He came on earlier than I planned but it was a case of needs must."
Palace manager Neil Warnock was fuming that referee Mark Clattenburg allowed West Brom's first goal to stand after goalkeeper Julian Speroni caught an elbow in the head from Craig Dawson.
However, Irvine believes that Palace's opener could also have been chalked off for a foul on Ben Foster.
"I have to say that on both [teams'] first goals my automatic reaction was to look at the referee to see what he was going to give," he added.
"On both occasions he didn't give a free-kick despite both goalkeepers ending up laying on their backs.
"It's always going to be debated when you have in-swinging corners and bodies going in there, we knew Palace would put them in like that, they probably knew we would too.
"The referee decided not to give a free-kick on either occasion."
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1