The Millers are bottom of the Championship having only won one game this season.
“It’s such an obvious handball. It’s not acceptable he can miss that,” Stubbs told BBC Radio Sheffield.
“He’s a former Premiership referee who should be getting basic decisions right.”
Stubbs added: “I hope the assessor wasn’t assessing him tonight. I thought there was a real lack of communication between referee and linesman.
“You had the linesman pointing for a corner, then suddenly raising his arm for a goal-kick.
“They were pausing for four or five seconds before making a decision. I thought they were pretty average.”
Rotherham equalised in the 34th minute through Danny Ward’s volley after trailing early in the game, but Huddersfield’s Nahki Wells scored just four minutes later to take the Terriers back to the top of the Championship.
“It was by far our better performance away from home but we’ve come away with nothing,” Stubbs continued.
“We have to do better. I’ll keep beating the drum until they get it right. We’re not good enough to give teams a start.
“I keep telling them you have to believe yourselves, without belief there’s no point in turning up.”