The event, which took place in Beverly Hills, California, highlighted achievements on television from the past year. Better Call Saul, now the second part of the sixth and final season, was a big winner of the night. Odenkirk, who plays Saul Goodman, spoke to PEOPLE ahead of the show.
"We're going to get together as a cast at somebody's house and watch the episode. And then we're going to cry," the actor says of how the ensemble will celebrate the end of the Breaking Bad spinoff on Monday.
Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.
Odenkirk tells PEOPLE the relationships with his fellow cast members are what has made the whole series experience so special.
"Rhea Seehorn, Michael McKean, Patrick Fabian, Michael Mando: This core group of actors are the best friends," Odenkirk, 59, says. "We're going to miss each other awfully."
The actor also notes the "unbelievable joy" he experienced working with TV icon Carol Burnett, who joined the series as a guest star for the final season.
"She's got chops in every direction, obviously," the actor gushes. "And she's gotten to show them yet again on Better Call Saul with her drama. And she's so heartbreaking. She's beautiful and heartbreaking and true and deep and fun and fun to be around. It was one of the heights of my career to be with her."
Odenkirk says he isn't going to try and top the many career highs Better Call Saul has given him, saying "you have to be careful."
"In show business, you can't guarantee that the next thing you do will be bigger than what you just did," Odenkirk explains. "Every project is an unsure endeavor so I'm more into doing something interesting that feels right."
The actor says it "may or may not be" a bigger project than playing Saul, but "it probably won't be."
"You try to stay with something interesting and challenging and you don't worry about whether it will be greater," Odenkirk says.
In his acceptance speech for outstanding actor in a drama aeries, Odeknirk joked about the quite serious setbacks the show experienced, saying, "pandemic, brief interlude with death — it slowed us down a little."
Fans know he was referring to his heart attack and recovery, which occurred last July, during the production of the final season.
In his speech, he revealed he "wasn't going to do this show." He said he was probably "just intimidated," but his two children convinced him to do it by saying it would disappoint a lot of people if he didn't. He finally decided to take the role when his wife assured him his family could "take care of things here at home."
Accepting the award on behalf of the show, Odenkirk said the show celebrates "fallible, complex human beings."
"One character, you're sure [he] is a bad guy, but then years later, you see him at a wine bar trying to connect with another human," Odenkirk said. "It's heartbreaking. You've got a guy who's clearly the bad guy, but wait a second, he's the best guy in the whole damn thing."
In his speech, the actor also thanked Peter Gould and Vince Gilligan for creating the show and for allowing him to share in their vision.
Better Call Saul won Best Cable Series, Drama; Best Supporting Actor in a Broadcast Network or Cable Series, Drama; Best Supporting Actress in a Broadcast Network or Cable Series, Drama; and Best Actor in a Broadcast Network or Cable Series, Drama.
The series finale of Better Call Saul airs Monday, Aug. 15 on AMC.