Midfielder Mooy scored a 25-yard winner for the Championship leaders.
But Monk was furious Mooy was still on the pitch, believing the Australian should have been given a red card and not a yellow for a lunging tackle on Liam Bridcutt in the first half.
"Two-footed, off the ground, totally out of control," Monk said of the foul.
"I don't want to talk about referees. But if you see that and you can't tell me that's a sending off, I don't know what is.
"It was a horrendous tackle that he made."
Huddersfield head coach David Wagner said Mooy's tackle was not worthy of dismissal in England, but would have been a straight red-card offence in his native Germany.
"In England no red card. Germany, red card," said Wagner, whose side are top of the table by four points after five wins from their six league matches.
"But we are not in Germany, we are in England. This is what I've learned. This was a pretty hard, British challenge.
"It came too late, but I didn't think for one second it would be a red card because I've been 10 months now in British football and I know, this was not okay, he was too late. Yellow."
Leeds boss Garry Monk said Huddersfield matchwinner Aaron Mooy should have been sent off for a "horrendous" foul in the west Yorkshire derby at Elland Road.