Clearly, Button also did not appreciate the comments.
"I think Ron is practicing to be a motivational speaker maybe," he told reporters ahead of his home race at Silverstone, where he will wear a pink helmet in tribute to his late father John.
"I don't think we should be pointing a finger at any individual within the team," said Button.
Button, 34, rejected Dennis' claim that he is not pushing to the maximum with the uncompetitive 2014 car.
But he said he is keen to race its 2015 successor, to be powered by a works Honda engine.
"I would like to stay," said Button, who is out of contract at the end of the season.
"This team has a bright future and the partnership with Honda will help the team a lot, having that connection with a manufacturer.
"But it isn't the only team in formula one," the Briton added.