Lenell John-Lewis stepped off the bench to give Bury all three points with a long-range effort in the 85th minute, but McIlroy was not too disheartened despite the defeat.
He said: "I'm absolutely devastated. We knew it was going to be difficult coming to Bury but I thought my lads were absolutely fantastic.
"The goal was the first shot Joe (Anyon) had to save and not long before that their keeper made an unbelievable save. Danny Carlton just missed one too, putting it onto the top of the net.
"I thought `well, if we come away with at least a point it's a fantastic result after the two wins we've just had'. But to concede a goal in that manner has just kicked my boys in the teeth because I thought they were magnificent, especially second half.
"I thought we deserved something but when you're fighting for your Football League status, these things happen. It's how we bounce back now and I've told my lads `show that effort and commitment and we'll stay in this league'."
Source: PA
Source: PA