Oghre was sin-binned with 18 minutes to go after making contact with the head of Mitchell.
It appeared to be a clear red card but referee Craig Maxwell-Keys decided it was only a yellow.
Saints went on to lose the game, and Boyd did not use the decision as an excuse for that, but he did feel Oghre should have been dismissed.
"There's no doubt it's a red card," Boyd said.
"I don't like the process particularly but you can't tell me a swinging arm to the head...
"I don't think there was any malice to it and I think it was unfortunate, but if that's not a red card, there is no red card.
"I just don't get it.
"He hit him with a swinging arm directly to the head.
"You might say there was less intent but I don't get it.
"We hold no malice to him (Oghre) because I think it was an accident, but at the end of the day, a lot of those things are accidental.
"It is what it is.
"It probably wouldn't haven't changed the end of the game because I think we were too dumb to take advantage of the gift we were given anyway."