The "Jeopardy!" host began with an anecdote about suffering two blood clots last year when he was also nominated for the award.
"I have worried about this moment. I was concerned that sympathy might play a big role in the voting this year. I'm not a big fan of sympathy votes. I believe that we should all be judges on the merits of our work," Trebek, 78, said.
"But then I started thinking back to last year. Last year I was nominated, and I had just had major surgery to remove to two life-threatening blood clots on my brain. You would think that would have elicited a certain amount of sympathy," he joked. "But I didn't win!"
"You guys like me, and you value my work. I tell you if that's the case, I can live with that."
Trebek later told The Hollywood Reporter backstage, “The reception I got from the audience was extremely special, very touching. We all know what’s going on in my life and I alluded to that in my remarks and I’ve been very blessed to discover how many people our show has influenced in their lives."
He continued, "'Jeopardy!' has become a special institution in Americana. And it has been a force for good, a force for knowledge, a force for the best kind of reality television if you think about it. Anybody can succeed, anybody can win a lot of money. Just ask James Holzhauer.”
Trebek revealed in March that he is battling stage 4 pancreatic cancer.
He said Saturday of his fight against the disease, "As you all know, survivorship is measured starting from the date you are diagnosed with cancer and on that scale — my gosh — I’m a 62-day survivor. Give me a break. But I’m working on it. And I promise you this: That if I become a 22-year survivor, you will all be welcomed at my 100th birthday.”