Alan, best known for playing the head of the Seaver family on the popular ABC sitcom, passed away after suffering a heart attack while playing hockey with Carter.
Robin, 39, said his father was "the greatest man I ever met" and said of his passing, "the good thing was that he was beloved and he had closure," reported Los Angeles Times.
The singer said he recently spent time with his father, during which he shared his great love and respect for him.
Carter posted his tribute on Twitter with a picture him and Alan.
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"Today I lost my best friend and my idol, and the world lost one of it's finest. You are a legend and I love you Pops. Until next time," he wrote on Twitter.
Just two days before his death, Alan's wife Tanya shared a photo on Instagram of herself looking adoringly at her husband. "I've got the cutest designated driver EVER!!!" she captioned the photo.
The veteran actor is survived by his wife, Tanya, and his three sons- Robin, Carter and Brennan.
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