The Baggies led twice through well-taken goals from Stephane Sessegnon and Saido Berahino but were denied by Marouane Fellaini, and then Daley Blind's strike as the game entered its closing stages.
He told the club's website after the game: "There are lot of positives to take we are disappointed that we got so close but didn't see the game out.
"We played very well for most of the game."
It has been a promising start to life for Irvine in the Premier League as the Baggies have shown they are capable of competing with sides who have ambitions to finish at least in the Champions League places.
Irvine's men left Tottenham Hotspur with all three points and competed well at Anfield, where the Baggies boss thought his side were unlucky not to come away with something from their game with Liverpool as they lost 2-1 prior to the international break.
But they only sit three points behind their more illustrious opponents from last night's encounter which represents a decent start to the season for Irvine's man, considering they have faced three of last season's top seven after just eight games.
At the moment they are a side playing with a great amount of pace and confidence with Sessegnon and Berahino both looking a big threat for their side - whilst defensive reinforcements in the summer in the form of Andre Wisdom on loan from Liverpool and Joleon Lescott have provided a good mixture of youth and experience.
After a last season's campaign where they battled for their Premier League survival, Baggies fans perhaps have more of a reason to be optimistic during the early signs of Irvine's reign.