Gunners boss Arsene Wenger described the tackle as "unacceptable" but Shawcross has been stoutly defended by Pulis and, also, a host of England's senior stars after gaining his first call up to Fabio Capello's squad this week.
"Ryan's been away and he's had a fantastic couple of days with England," said Pulis.
"I've made sure I've spoken to him every day and he has been fine and the players have been fantastic.
"Steven Gerrard, apparently, has been exceptional and as the captain of the team has really looked after him.
"People like Wayne Rooney and David Beckham have been brilliant and I think Shawcross will be the first to say how much help he's had from the players.
"Beckham has been very good with him, like they all have. It's the first time he has been called up for England and I think they do it with most of the lads.
"They are human beings and they know he is new to the squad, irrespective of what happened on Saturday, and that he will need some help."
Pulis said although he did not feel Shawcross' tackle was malicious they had decided not to appeal against his three-match ban as they wanted to put an end to the matter as soon as possible.
"I don't think it is an incident we want to bring up again," added the Potters boss.
"We'll take our medicine. It was an awkward challenge, not a dirty challenge and there was no vindictiveness.
"But we'll take our punishment as I think we have to move on and that is what we'll do."
Pulis is not concerned the England Under-21 international will have any problems getting straight back into action after his suspension.
"We'll speak to Ryan when he comes back because we have not had time to sit with him face to face," he added.
"He has got to come back now and make sure he works hard and gets himself back on that pitch.
"But we have to make sure Ryan understands it was an accident more than anything malicious and vicious and he has to move on.
"Ryan will get looked after at this club. We'll do our damnedest to make sure he gets over this unfortunate incident."
Both Pulis and Shawcross have spoken to Ramsey and received a positive response and there have also been high-level talks between chief executive Tony Scholes and Arsenal in a bid to smooth over relations between the two clubs.
In the past, Wenger had claimed Stoke players had tried to injure his squad and Saturday's incident only stoked his claims of a conspiracy to target Arsenal.
Pulis said those allegations were unjustified and the club wanted to draw a line under the whole matter.
"We've been in contact with Aaron both myself and Ryan and we will continue to do that through his recovery period," he added.
"It has been smashing, it has not been a problem.
"I think Tony has spoken to the powers that be [at Arsenal] but the most important thing for us here is the kid and it always has been the kid."
On Wenger's allegations, Pulis added: "We have played Arsenal three times this year and apart from Ryan's sending-off we haven't had one player booked.
"That doesn't sound like a team who go out to injure people. We are desperately disappointed."
Chelsea 3/10, Draw 4/1, Stoke 9/1