"No one admires what he accomplished more than I do," Sajak, 74 said of Trebek. "I know a bit about what it takes. He was terrific. In terms of courage and grace under pressure, no one was better."
Video: Celebrating the life of beloved television host Alex Trebek
"I knew Alex for almost 40 years, and he's just been a good friend," shared White, 63. "Through the years, I have gotten to know his wife and his kids and he is just part of the family."
Sajak chimed in, "Just on a professional level, I have been at this a long time and I really admire what he has done, and he had done so much."
"When I started [Wheel of Fortune]... Alex had already done a half a dozen, maybe more, game shows here and in Canada," he added. "He has done a bunch of them, and was always highly professional and was like the perfect match for his show... As a fellow professional, the admiration is off the charts."
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Trebek died on Nov. 8 at age 80 after suffering from stage four pancreatic cancer.
Trebek's final episodes of Jeopardy!, which were taped shortly before his death, have been airing this week. On Friday, Jan. 8, Trebek will sign off in his final episode.
Beginning Monday, Jan. 11, former Jeopardy! champion Ken Jennings will begin his stint as guest host, while producers decide who will take over permanently for Trebek.
Jennings, recently told PEOPLE the experience has been "dizzying," and knows that viewers will probably have a hard time seeing him at the podium instead of their beloved Trebek.
"I understand better than anybody that these are very big shoes to fill," he told PEOPLE for this week's issue. "I expect people to be a little discontented when they see me. I'm right there with them. The only thing I can do is to try doing the job the best I can."