Jonathan de Guzman put the hosts ahead in the 25th minute as Swansea dominated the opening period, but they failed to build on that advantage.
Chico Flores was then sent off after he was adjudged to have fouled Glenn Murray in the penalty area 10 minutes from time, allowing the Palace striker to haul his side level from the spot.
However, television replays indicated that the initial contact had actually occurred outside the box, and Monk questioned whether Dean had a clear view of the incident.
"(It was) 100 per cent outside the area, so for me, why is the referee making the decision from 60 yards away that he clearly has no view of being able to tell that?" said Monk.
"He hasn't conferred with his assistant. I looked straight at him and he didn't confer with his linesman.
"The linesman's not flagging for anything, not flagging for a penalty.
"So he's decided to make a bizarre decision.
"It was like he couldn't wait to give the penalty and then he couldn't wait to give the red card.
"The penalty - without a shadow of a doubt - is not a penalty."
Swansea's dominant display waned in the second half at the Liberty Stadium and Monk revealed that some key players had been struck with illness in the build-up to the match.
"We've had illness in the camp the last few days," he added. "(Wilfried) Bony's been ill, Ash (Williams) was sick all last night and didn't sleep, and you're asking these guys to go out and play 90 minutes.
"Ash has (also) got two very badly bruised toes and it just shows you the character that he is, the leader he is, that he continues to play and they all did it.
"They've all got knocks and bruises.
"I think it's all a bit of what we've been going through this month and the amount of games that we've had. I'm not making excuses, I'm just telling you how it is."
