Hojbjerg was sent off for a second yellow card, with referee Jonathan Moss adjudging the Saints midfielder to have dived.
"The first yellow card was harsh, it was just a coming together, it wasn't even a foul," Hughes said of the Hojbjerg incident. "However, if you are in that situation, Pierre knows he has to be careful.
"He did get a clip just prior to going down. That affected his momentum and at one point. I think he thought he could get a shot off, and when he thought he couldn't, he then did go down a little bit easily. Mr Moss was on the spot to send him off very quickly.
"It did change the game. I thought we were excellent from start up until the sending off. First half was arguably one of the best performances we have had, certainly at St Mary's. We should have gone two or three goals to the good coming into the half-time period."