Murray acknowledged Mr Cameron in an on-court interview as he collected his second Wimbledon title on the nation’s greatest weekend at the All England Club.
As the camera panned to him, Mr Cameron managed to laugh off the moment, which was reminiscent of the chorus of boos that Chancellor George Osborne suffered at the 2012 London Olympics.
In a live question and answer session on Facebook, Murray said: “Did I mean to embarrass Cameron? No I certainly didn’t.
“I appreciate he came to support yesterday and came to watch and like I said afterwards - it’s one of the hardest jobs in the world with lots and lots of responsibility.
“I don’t envy anyone who is in a position like that - it’s extremely difficult.”
Mr Cameron had joined actors Bradley Cooper and Benedict Cumberbatch and Scottish First Minister Nicola Sturgeon in the Royal Box, while the player’s wife Kim and his mother Judy shouted their congratulations from his player’s area.
British players won five trophies during the Championships’ finale, taking home the silverware from every final they were in.
Murray led the charge in SW19, leaving the Duke and Duchess of Cambridge and the other guests in the Royal Box in raptures with his straight sets victory over Canadian Milos Raonic.
But there was also triumph for Heather Watson and her Finnish partner Henri Kontinen in the mixed doubles, Scot Gordon Reid in the inaugural Wimbledon men’s wheelchair singles and in the doubles with Norwich teenager Alfie Hewett, and Jordanne Whiley, who tasted victory in the final of the ladies’ wheelchair doubles.
This morning he admitted he was feeling “tired” after his celebrations and he was looking forward to a few days’ rest.
He said: “I had a rough night last night, good celebrations with the teams, it was good fun.”
He added the win felt “a lot nicer” than his first Wimbledon victory because he was “calmer and a lot happier”.
After his win, William and Kate congratulated the 29-year-old as he clutched the trophy to his chest.