The Potters' 43rd-minute equaliser in the Britannia Stadium contest came from a penalty awarded when Moses went to ground - a little easily, it appeared - as he was challenged in the box by Angel Rangel.
Enraged Swans boss Garry Monk was strongly critical of Moses and referee Michael Oliver after the game and it is understood his comments are being studied by the Football Association to see if the manager should face any action.
Swansea-born Hartson, giving his view on Match of the Day 2 on Sunday night, echoed some of what Monk said in terms of labelling Moses a cheat who should be punished for a "blatant dive".
Hartson said: "That for me is a terrible dive and a total lack of professionalism from Moses
I think Garry Monk has a right to be angry
He (Moses) has cheated.
"It's one thing the FA coming out and charging Garry Monk - what about charging Victor Moses for diving?
"I would (charge Moses) because you can't dive
That is a blatant dive."
Coates responded on Monday by describing Hartson as a "disgrace", and it has been reported that he is making an official complaint to the BBC over the matter.
"I've never heard a more one-sided view from a pundit and we are right to complain about it," said Coates, quoted by The Sentinel.
"Hartson was a disgrace
He's a big fan of Swansea and their manager..
and it showed."
He added: "Whether Garry Monk likes it or not, it was given
It probably was soft, but we've had our fair share of things go against us in the past.
"(Stoke striker) Peter Crouch has arms wrapped around him every single game and (Match of the Day presenter Gary) Lineker doesn't say anything about that."
But Hartson has defended himself on Twitter and insisted he has nothing against Stoke and was merely commenting on the situation as he saw it
He tweeted: "I have nothing against Stoke, certainly Nothing against Mark Hughes or Victor Moses I am simply making a comment on an incompetent decision."
Meanwhile, Stoke goalkeeper Asmir Begovic has defended Moses, the winger who is on loan with the Potters from Chelsea
Begovic told Sky Sports News: "We know Victor and we see him each and every day.
"I don't think those kind of labels are fair.
"I know it is in the aftermath of a game and I know Swansea are angry about losing
I don't think it is ever pleasant.
"But to call a player a cheat is a little bit over the top and I don't."
Source : PA
Source: PA