The Prime Minister said he wanted to create a "good relationship going forward" with the incoming US President.
Mr Trump met Sir Keir in New York last month before it emerged that Labour staff had campaigned for his rival Kamala Harris.
Some Labour frontbenchers also made personal attacks on the President-elect while in opposition.
Constructive
When Sir Keir was asked whether he was surprised to have got on well with Mr Trump, he said: "No, because my approach is to ensure that I have good relations with leaders across the world.
"The best way to build good relations that are based on trust and respect is face to face.
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