Trump attacked Saturday Night Live and Baldwin's impersonation shortly before last year's vote, tweeting: "Time to retire the boring and unfunny show".
"I don't know", Baldwin said.
"This is the biggest audience to witness an Emmys, period", Spicer said, standing behind a lectern.
At the top of the Emmys, host Stephen Colbert welcomed Spicer on stage to jokingly assess the audience size. He referred to the point that Trump didn't win an Emmy for his show The Apprentice. I'm the first African-American in 16 years nominated.More news: Police deploy in Iraqi oil city Kirkuk after deadly clash
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At one point, Julia Louis-Dreyfus showed up in the guise of her "Veep" character Selina Meyer.
He claimed that what Hollywood and other performers do is important and they should "not stop doing what (they're) doing". Netflix's anthology series "Black Mirror" won two awards, including best TV movie for its episode "San Junipero".
This is Baldwin's third Emmy win, having previously won for lead actor in a comedy for his work on "30 Rock".
"SNL" has a good night: "Saturday Night Live", like the nighttime talk shows, has capitalized on the 2016 election to huge success. Earlier in the evening, Kate McKinnon was visibly emotional as she picked up the Outstanding Supporting Actress in a Comedy Series accolade for her portrayal of Trump's Democratic rival Hillary Clinton on "SNL". Trump took a verbal beating throughout the night, sure, but this comment is surely the most scathing. "And they walk up to me and slap me on the back all day long and say, 'Thank you, thank you, thank you'". Fan favorite "Stranger Things" won just five of its 18 nominations, mostly in technical categories, and British royal series "The Crown" came away with three out of 16 nominations.