(CNN) There was plenty of talk about diversity in Hollywood on Monday night at the 70th Primetime Emmy Awards, but the talk did not translate into wins for performers of color.

The show kicked off with an entire skit about how diverse this year's nominees were and how Hollywood had solved its race issue.

"Saturday Night Live" cast members Kate McKinnon and Kenan Thompson did a jokey song and dance number titled "We Solved It."

"This year's Emmy Awards has the most diverse group of nominees in Emmy history," Thompson said. "Yes, indeedy. One step closer to a black Sheldon. I'm going to go ahead and say it: We solved it."

They were joined by Ricky Martin, RuPaul, Kristen Bell, Tituss Burgess, Sterling K. Brown and Andy Samberg to point out all the ways Hollywood had overcome a lack of inclusion -- and yet not.

Had either Issa Rae or Tracee Ellis Ross won for outstanding lead actress in a comedy, it would have been only the second time an African American woman won the category since Isabel Sanford for "The Jeffersons" in 1981.

The award went to Rachel Brosnahan for "The Marvelous Mrs. Maisel."

Sandra Oh made history as the first woman of Asian descent to be nominated for lead actress in a drama series this year and joked during the opening skit that it was "an honor just to be Asian."

Thompson responded with "You see? There were none, now there's one!"

Oh did not win.

During their opening co-hosts Michael Che and Colin Joust got in some jabs as well, with Che joking that his mother didn't watch the Emmys because it was mostly white people and they "don't thank Jesus."

After the first awards were given Che noted, "Six awards, all white winners. One lady won twice...No one thanked Jesus."

Actress Regina King played off that joke when she won outstanding lead actress in a limited series or TV movie for her role in "Seven Seconds" and made sure to thank Jesus.

One of the biggest hits of the evening was Che's skit about the "Reparation Emmys," which featured Marla Gibbs from "The Jeffersons" and "227," Kadeem Hardison from "A Different World," and John Witherspoon from "The Wayans Brothers."

Che joked that the Emmys he gave out were awards taken back from Bill Cosby.

Thandie Newton, whose mother is black, and Darren Criss, whose mother is Filipino, were also among the actors of color to win on Monday night.

Speaking to CNN on the red carpet ahead of the Emmys, actor John Leguizamo, who was nominated in the supporting actor in a limited series category and one of the few Latinos to score a nomination, acknowledged that there had been "some change" to include more people of color, but said it is "not as much as I'd like to see."

"We Latin people are 50% of people in LA and less than three percent of our faces are on camera," he said.

The solution is "easy," he added.

"The talent is out there. The people are out there," he said. "We need to have executives who are Latino who are making those choices, who understand our culture and who are making the right decisions."

Heading into the Emmys, there was reason to be optimistic about the possibility of more inclusive winners.