In an interview on Monday morning, Mr. Spicer said he now regrets one of his most infamous moments as press secretary: his decision to charge into the White House briefing room in January and criticize accurate news reports that Barack Obama’s inauguration crowd was bigger than President Donald J. Trump’s.

“Of course I do, absolutely,” Mr. Spicer said.

For Mr. Spicer, who resigned this summer after repeated clashes with the news media and a sharp disagreement with President Trump over the appointment of Anthony Scaramucci as communications director, the Emmys were his latest attempt to ingratiate himself with the largely liberal coastal entertainment and news elites he so acidly disdained as Mr. Trump’s alter-ego spokesman. The once-obscure party spokesman has been elevated to a level of celebrity he scarcely dreamed possible a year ago and, like many before him, he hopes to translate his notoriety into something more reputable and lucrative. So the Emmys were also a chance for Mr. Spicer to cultivate a television industry audience that he may need as he seeks speaking engagements and paid television appearances in his post-White House life.