Trump's frequent tweeting was raised by Lauer in a telephone interview on the Today show following Time magazine's selection of the president-elect as its Person of the Year.
"Can we agree, President-elect Trump, that it would be better for you to simply stop watching SNL as opposed to watching and then complaining about it?" Lauer said.
His question was no ad-lib, since NBC quickly aired clips of the Baldwin-McKinnon sketch as Trump replied.
"I hosted SNL when it was a good show but it's not a good show anymore," said Trump, who also took a turn as guest host in 2004. "First of all, nothing to do with me, there's nothing funny about it. The skits are terrible. I like Alec, but his imitation of me is really mean-spirited and not very good ... It's very biased and I don't like it."
And yet, Lauer noted, he still watches.
"You look at the way the show is going now and the kind of work they're doing, who knows how long the show is going to be on? It's a terrible show," Trump said.
Fact check: Saturday Night Live is in its 42nd season and enjoying its best ratings since 1992, the Nielsen company said. Viewership is up 33 percent over 2015.
The attention paid by Trump certainly hasn't hurt, said NBC Entertainment Chairman Bob Greenblatt.
"I love the fact that SNL has this position of being able to have a lot of impact on current events and that the world turned to the show in record numbers this past fall to see how they were going to comment on what was going on and bring comedy to that," Greenblatt said.
The show's founding executive producer, Lorne Michaels, would not comment on Trump's statement, a spokeswoman said. Michaels, awarded the Presidential Medal of Freedom by President Barack Obama two weeks ago, hasn't reacted publicly to the criticism by the soon-to-be leader of the free world.
Baldwin, whose portrayal in a skit that satirized Trump's tweets was dubbed "sad" by Trump in last weekend's late-night tweet, responded via Twitter: "Release your tax returns and I'll stop. Ha."
"There are certain things that come with the presidency -- the football with the (nuclear) codes, Air Force One and being parodied on Saturday Night Live," said James Andrew Miller, co-author of Live From New York: The Complete, Uncensored History of Saturday Night Live. "He should just relax and get used to it."
The unprecedented high-level attention is nothing but good for the show, Miller said. It reminds Trump's Twitter followers who might not be regular viewers that SNL is still around and relevant, he said. A rebellious reputation also can't hurt a show that's been alive for longer than most of its viewers, many of whom would find Trump criticism to be a thumbs-up.
Miller said he didn't believe that the knowledge that Trump is keeping his eye on them would make the show and its writers self-conscious.
"Lorne has a laser focus on the fact that there should be no other agenda but to be funny," he said. "I don't think they're going to ... try to do any political messaging in response to what (Trump) is doing."
Trump, of course, has a long history with NBC. His host appearance last fall was not welcomed by several cast members or Trump's Republican primary opponents, who lobbied for equal time.
The president-elect's also owed much of his public profile to his years as host of NBC's The Apprentice. In fact, Trump made his announcement that he would not run for president in 2012 at a presentation NBC was giving to advertisers about its fall schedule. The network cut ties with Trump shortly after he announced he was running for president in June 2016.