Mrs May said that “absolutism” fuelled by a coarsening of online debate and the rise of populist politics meant that democratic values were at risk.
And in a message to her successor, she warned against "making promises you can't keep or... telling people what they want to hear" as she made a final appeal on behalf of her Brexit agreement.
"And a healthy body politic will be essential to consolidating and extending that progress in the future.
"It is on that score that today we do have grounds for serious concern. Both domestically and internationally, in substance and in tone, I'm worried about the state of politics.
"That worry stems from a conviction that the values on which all of our successes have been founded cannot be taken for granted."
The Prime Minister added: "Today, an inability to combine principles with pragmatism and make a compromise when required seems to have driven our whole political discourse down the wrong path.
"It has led to what is, in effect, a form of absolutism. One which believes that if you simply assert your view loud enough and long enough you will get your way in the end.
"Or that mobilising your own faction is more important than bringing others with you. This is coarsening our public debate."
Mrs May said: "Some are losing the ability to disagree without demeaning the views of others.
"This dissent of our debate into rancour and tribal bitterness, and in some cases, even vile abuse at a criminal level, is corrosive to the democratic values which we should all be seeking to uphold."
She added: "Words have consequences. And ill words that go unchallenged are the first step on a continuum to ill deeds. Towards a much darker place where hatred and prejudice drive not only what people say but also what they do."
Mrs May warned that the international organisations established in the wake of the Second World War could not be taken for granted.
"The current failure to combine principles with pragmatism and compromise inevitably risks undermining them," she said.
The impact of the financial crisis had brought "years of hardship from which we are only now emerging", she added.
"Populist movements have seized the opportunity to capitalise on that vacuum. They have embraced the politics of division, identifying the enemies to blame for our problems and offering apparently easy answers."