Payne was one of seven Gillingham players booked when he made an ill-advised lunge on Romain Vincelot.
Hessenthaler told BBC Radio Kent: "I've got to say that's a straight red. That's why I went up to Gus [Poyet] when it happened, he should have gone."
Payne's tackle prompted a brief skirmish on the pitch as tempers frayed in the closing stages.
Hessenthaler admitted afterwards that Payne was fortunate to remain on the field.
"He was a lucky boy. He lost his head and he can't do that," he said.
"We can't afford to lose players in games. He'll learn from that."
However Hessenthaler defended the actions of his players following the bad-mannered cup tie, insisting his side were competitive rather than dirty.
"We lost our discipline a little bit but we're competitive," he added. "We're a competitive team that came and tried to go up against a Championship side and more than match them."
Source: BBC Sport
Source: BBC Sport