The Prime Minister's criticism comes as the President-elect says he is "very much" looking forward to meeting her this spring.
Theresa May has told Sky News Donald Trump's lewd remarks about women were "unacceptable" ahead of meeting him this spring.
Speaking to Sophy Ridge on Sunday in her first TV interview of the year, the Prime Minister was critical of offensive comments previously made by the President-elect, but pointed out he had since apologised for them.
Mrs May also said she believed the US remained "fully committed" to NATO, despite Mr Trump's criticism of the military alliance, which he has described as obsolete.
Mr Trump faced an angry backlash during last year's presidential campaign after a 2005 recording emerged of him boasting about groping women and that he could "grab them by the pussy" because of his celebrity status.
Mr Trump faced an angry backlash during last year's presidential campaign after a 2005 recording emerged of him boasting about groping women and that he could "grab them by the pussy" because of his celebrity status.
Asked by Sophy Ridge about her response as a woman to the comments, Mrs May 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 tweeted he was "very much" looking forward to meeting the PM, adding that he considered Britain to be a "very special" ally - a signal the "special relationship" between the US and the UK will be maintained under his administration.
The pair are due to meet in Washington in the spring after the PM's closest advisers travelled to the US in December to forge links with the President-elect's team and pave the way for the visit.
A date for the mini-summit is yet to be announced, but it is expected to come within weeks of Mr Trump's inauguration on 20 January.
Mr Trump wrote on Twitter: "I look very much forward to meeting Prime Minister Theresa May in Washington in the Spring. Britain, a longtime US ally, is very special!"
Mr Trump's warm words will be welcomed by Downing Street after so much attention has focused on his close relationship with former UKIP leader Nigel Farage.
Mrs May was upbeat about the future relationship with the White House, which is seen as vital as the UK prepares to break with Brussels.
She said: "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.
"I think that is something that is optimistic and positive for the UK for the future."
Mrs May also indicated her confidence in the US commitment to NATO, despite Mr Trump's comments and his praise for the Russian President Vladimir Putin.
She said: "Sometimes people think that there is going to be a change in the American approach to NATO.
"From the conversations I have had, I think America remains fully committed to NATO as we do."