Irvine's men led twice at The Hawthorns and only conceded for a second time in the 87th minute when United midfielder Daley Blind found the bottom right corner of Boaz Myhill's net from the edge of the penalty area.
In a perfect illustration of how well his team had played, Irvine could only shake his head in frustration when asked how he felt to miss out on three Premier League points at home against United.
The Scottish manager made it clear he felt West Brom would have deserved the win if they could have held on.
"At times we passed the ball extremely well, the two goals we got were great goals and, you know, we've led twice and to be honest I've felt quite comfortable when we were leading," he told Sky Sports.
Irvine added it was tough to end the game with just a draw.
"We're all bitterly disappointed," he said.
"We were so close to getting a great result against a top team and for us to not get the three points feels really tough at this point. The players were terrific all the way through."
West Brom stunned United early in the match with Stephane Sessegnon thumping the ball past David de Gea in just the eighth minute but the visitors equalised two minutes after the break when Marouane Fellaini controlled the ball on his chest and then finished from a tight angle.
But the hosts would lead again with Saido Berahino continuing his top form with a fine one-on-one finish in the 66th minute, only for Blind to snatch a draw for United with three minutes left.
Irvine tried to remain diplomatic but he admitted he felt Fellaini had fouled West Brom defender Joleon Lescott in the lead-up to United's first equaliser.
"I looked straight away at [referee] Mike Dean to see whether he was going to give a foul or not," Irvine said.
"There's no doubt Marouane Fellaini bumped Joleon Lescott, while the ball was in flight. The fact that I looked at him, indicates I thought it might have been a foul.
"He didn't give it and we just have to accept that didn't happen and it was a great finish by Marouane."
