Mr Trump’s presidential campaign was plunged into crisis after a 2005 tape recording came to light of him bragging to TV host Billy Bush about groping women because of his celebrity status.
Mrs May was asked how the comments made her feel as a woman during her first broadcast interview of the New Year.
She said: “I think that’s unacceptable, but in fact Donald Trump himself has said that and has apologised for it.
“But the relationship that the UK has with the United States is about something much bigger than just the relationship between the two individuals as president and prime minister. That’s important, but actually we have a long-standing special relationship with the United States.
“It’s based on shared values and it is a relationship where, actually in the UK, we feel we can say to the US if we disagree with something that they are doing.”
Mr Trump has said he is “very much” looking forward to meeting Mrs May in the coming months and described Britain as a “very special” ally.
The pair are due to meet in Washington in the spring following preparatory meetings by her closest advisers over the Christmas period.
Mr Trump wrote on Twitter: “I look very much forward to meeting Prime Minister Theresa May in Washington in the. Britain, a long-time US ally, is very special!”
A date for the meeting is yet to be revealed, but it is expected to come within weeks of Mr Trump’s inauguration on January 20.
The status of the special relationship between the two long-time allies has faced fierce speculation ever since Mr Trump won the US presidential election.
That speculation has been fuelled by the president-elect’s close relationship with the former Ukip leader Nigel Farage. But Mrs May insisted she envisages a bright future for the countries.
“From the conversations I have already had – I have had two very good, positive conversations with Donald Trump already – I think we are going to look to build on that relationship for the benefit of both the US and the UK,” she said.
“I think that is something that is optimistic and positive for the UK for the future.”