Boro snatched the points when a speculative Scott McDonald shot took a wicked deflection just before the break.
"We are extremely disappointed," Irvine admitted. "We did enough to come away with something.
"The goal was very cruel on us. I felt we were the better team for most of the game.
"Boro were a threat on the counter-attack, especially as the game wore on, but we had the chances to win it.
"I lost count of the number of times their defenders dived in to block shots from going in. We came close on a lot of occasions but maybe we didn't directly test their keeper often enough."
With time running out, Wednesday remain in the bottom three and Irvine admits it is now down to other results.
"It is out of our hands now," he said as he prepared for a big derby against Sheffield United next week.
"We have a massive derby clash coming up now and everyone here is aware exactly how important it is.
"If the rest win their last three games then we'll go down - but if we can win our last three and one of them slip up somewhere then we'll be safe.
"I said when I came here it would go down to the last game and nothing has changed."