Dick hugged Sharna Burgess, his pro dance partner, and held her tight after learning of his elimination.
"We thought maybe with those low scores our time might be up, but we had such a strong fan base we thought maybe we'd get another week, which of course we didn't," an emotional Dick explained this morning on "Good Morning America."
Burgess, also a rookie to the show, said she couldn't have asked for a better partner for first season, praising Dick's personal depth.
"He's just such an incredible soul and loveable person through to his core," said Burgess. "This has been the most memorable experience I could have ever wished for on a first season. Not just having a wonderful season, but finding a best friend."
Dick was overcome with emotion Tuesday night as he talked about what the experience had meant to him.
"It's been the best. It's just been the best," he said, his voice breaking.
He jokingly told judge Carrie Ann Inaba that the result was her fault because she gave him a low score - a 5 out of 10 - for his individual routine on Monday night, and he thanked his cast mates, the show's judges and hosts, and the fans who supported him.
"The fact that we're here on week seven is amazing," he said, adding that every week he was amazed when he got the chance to remain in the show.
Dick's children surprised him with a video message of support this morning on "GMA."
"We love you so much daddy," they said. "You did really good for a non-dancer on a dance show. And it doesn't mean you should stop dancing. Keep it up. Dance for us. Team Dick!"
Throughout the seven weeks of competition in season 16, judges commended Dick for his upbeat approach, dedication to his routines and his highly entertaining performances, but they acknowledged his shortcomings in technique, fluidity and musicality. Dick has often been at or near the bottom of the leaderboard, and ended up in last place after his two performances on Monday night.
Dick and soap opera star Ingo Rademacher had both been in jeopardy of being eliminated Tuesday night based on their performances on Monday, but Dick had the lowest combined tally of judges' scores and viewers' votes, so he was sent home.
Country music singer Kellie Pickler won immunity on Monday, so she could not be eliminated Tuesday.
Tuesday's show featured live performances from Michael Bublé.
Returning next week to perform to compete are Pickler, Rademacher, reality TV star Sean Lowe, Olympic gymnast Aly Raisman, Disney star Zendaya and NFL player Jacoby Jones.
Boxing champion Victor Ortiz, comedian D.L. Hughley, country music legend Wynonna Judd and reality TV star Lisa Vanderpump have already been eliminated this season. Figure skating legend Dorothy Hamill withdrew from the competition because of an injury.