The 78-year-old actor - who led the cast as bar owner Sam Malone - recalled how the program was a hit with critics when it debuted in 1982 but struggled to find an audience, even coming "dead last" in the ratings at one point.
"Critics loved us. Everyone around us…the writers, everybody was so positive. 'Don't pay attention, just keep doing it' kind of feedback, which was lovely, but we were dead last one week in the ratings," he told the Dinner's On Me podcast.
"We were like... Jimmy (Burrows) likes to say we were 75th outta 70. There were only 70 shows."
Danson was later told NBC "would have" scrapped the program but "they had nothing to replace Cheers with".
Cheers went on to run for 11 seasons, winning six Golden Globe awards and 28 Primetime Emmys, before spawning spin-off show Frasier.
And once the program became an established favourite, Danson's parents started tuning in.
"My father always thought I should get a teaching degree in case it didn't work out. My mom was just thrilled. She was a grand appreciator," he said.
"So they were happy, and then they bought their first TV so they could watch Cheers."
"They got hooked. They got suckered into it, you know. So they bought one of those huge TVs that's like a piece of furniture."
Cheers co-creator James Burrows previously revealed the show would have ran for much longer if the Three Men and a Baby actor hadn't been ready to do new things.
"If Ted had wanted to stay, we would have kept going," he told Entertainment Weekly:.
"The (cast) had the best jobs in the world. We were still on top. Regardless, they were all wonderful characters who could carry their own show."
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