The match official failed to send off Wednesday midfielder Jeremy Helan for a second yellow-card offence during the first half.
"As we came off the pitch at half-time he came to me to apologise for the error he made," said Grayson.
"I think he's probably written the wrong number down in his book, which is staggering.
"I also think he should have been helped by his officials, who should be overruling because they all know, when a referee makes a mistake like that, who he's booking.
"The linesman should be helping out. He's not done it deliberately, but you can't make major mistakes like that.
"He's put (Michail) Antonio's number in his book, but he was nowhere near the incident.
"I don't mind referees making big mistakes in terms of tackles and sendings off, but something quite simple like that shouldn't be happening in Championship football."
When it was suggested Huddersfield might have grounds to replay the match Grayson added: "I'm not sure about that. No-one has said anything like that. I'd be very surprised.
"It's a shame, we shouldn't be talking about the referee after a Yorkshire derby, with a great atmosphere and two teams trying to win a football match."