Scott Spencer's injury-time penalty earned Hyde a point at Wrexham in an incident-packed game.
The hosts fell behind to Tom Collins's penalty after Brett Ormerod felled Louis Almond but fought back through Kevin Thornton and Junior N'Tame.
But Wrexham were reduced to 10 men in the 40th minute when Jay Harris was sent off for lashing out with a boot.
They looked set to hold on but N'Tame was judged to have handled in the penalty area and Spencer struck.
VIEWS FROM THE DRESSING ROOM
Wrexham manager Andy Morrell told BBC Radio Wales: "I'm struggling to speak… because I don't really know what to say.
"Dumbfounded at what I've just seen. I've just watched the first penalty and I don't think it's any over-exaggeration that I think it's the worst decision I've ever seen in football.
"If anything it's a foul on Brett… and then I'm gutted for the lads because they've dug in and [Hyde] haven't really created anything in the second half and then four bodies go up for a header, they come down in a heap and somehow the linesman that's 30 yards away sees it and gives it [the second penalty].
"I haven't seen it [Jay Harris' alleged red card offence]. I missed it. If he's kicked out… when he's been on the floor then he deserves it.
"And he's on three yellow cards and he's got a red today and it seems like it's just been coming - ill discipline by him and he's let everybody down and he knows that; he's held his hand up."