Town defender Dean Holden put the ball into his own net in the seventh minute before a further strike from James Spencer and a Laurence Wilson penalty put the Shrimps three goals to the good.
Spencer was dismissed for violent conduct and the Shrews pulled one back thanks to Shane Cansdell-Sherriff, however it mattered little as Morecambe held on for victory.
McIlroy said: "The first half was excellent. In fact we let Shrewsbury off the hook at only 2-0 at half-time. Then when we got the penalty just after half-time and I thought that if we played properly the game is over.
"But all of a sudden we got a man sent off and gave Shrewsbury a little bit of a lift. We had to hang on for long periods but showed spirit and the whole of the back four were magnificent."
On Spencer`s sending off, McIlroy added: "There was a skirmish and Dean Holden has been totally honest and said it wasn't a stamping. The two were niggling at each other but unfortunately the assistant referee saw Jimmy sort of flick out at the boy and it was a bit harsh but the kid's got to learn. Hopefully the referee will take a look at the video and maybe he won't have a three-match ban."
Source: PA
Source: PA