The Baggies led twice at The Hawthorns before a late goal from Daley Blind denied them a third victory of the campaign which Irvine feels was a little bit of an injustice.
"We're all bitterly disappointed. We were so close to getting a great result against a top team," he told Sky Sports.
"For us not to get the three points feels really tough at this moment. The players were terrific all the way through.
"They worked really hard when we didn't have the ball and at times we passed the ball extremely well.
He added: "The players are doing really well. They're a great group and do all the things that we ask them to do.
"It's all very well to work on the things in the training ground; it's a lot more difficult when it's out in front of the cameras and the fans, and against Manchester United."
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