The singer was among the favourites to win the contest outright when the show began and joked she had made her husband promise to have a vasectomy if she won the dancefloor challenge.
But Phillips' run on the programme ended on Tuesday and her shock exit caught Baldwin off guard.
Speaking to TV show Access Hollywood minutes after the elimination, he said, "I'm so proud of Chynna." He then had to halt the interview to compose himself.
Phillips' dance partner Tony Dovolani helped lighten the mood, by stating, "One bright side is Billy doesn't have to snip his b**ls."