In an interview released on Friday, Trump also described Clinton as "very strong and very smart", the New York Post reported.
"So, Hillary called, and it was a lovely call, and it was a tough call for her, I mean, I can imagine," Trump said.
"She couldn't have been nicer. She just said, 'Congratulations, Donald, well done'. And I said, 'I want to thank you very much, you were a great competitor'," he added.
Trump's surprise win in Tuesday's presidential election, sent shockwaves all across the world.
He will officially take over as the 45th US President on January 20, 2017.