The allegations came after Jones told Sky Sports News that some players were happy Tony Pulis was no longer at the club.
However, Shawcross insists there are no issues amongst the squad and that team spirit remains 'fantastic' under Pulis' successor Mark Hughes.
"It's the old cliche of don't always read what's in the papers, it is not always truthful," he told Sky Sports News.
"I think that is what has happened here - nothing really went on to be honest and team spirit stays as it always has been, fantastic.
"There are no problems with anyone and we are just enjoying our football with the new manager."
Shawcross insists that people should not forget what former boss Pulis did for Stoke.
"People are quick to forget what he did in his time here, he was fantastic," he said.
"I really enjoyed it underneath him and he will be remembered for a long time, but now we have moved onto the new manager and everyone can see the style has changed.
"Luckily the performances have come with it because, when you change your style like that it can be difficult to get results, but we seem to have hit the ground running."