"I just hope people realize what a great baseball man this guy was," said Jim Leyland, another of Zimmer's closest friends and the former manager of the Pirates, Marlins, Rockies and Tigers. "I want people to remember how good he was."
"He was one of a kind," said Torre, who hired Zimmer to be his bench coach when he managed the Yankees. "Baseball is going to miss the presence of this man. He was a teddy bear. His loss leaves a big void in my life."
"'I'd put him on the same level with Yogi Berra," Torre said. "You look at Yogi and you'd look at Zim and it put a smile on your face. Everybody knows who Don Zimmer is. And he knew everybody in baseball. His knowledge of this game was tremendous."
Zimmer played with, managed or coached 1,254 Major League players from 1954 to 2014 -- nearly seven percent of all players in baseball history. He also played with, managed or coached 28 of the 211 players (13 percent) in the Hall of Fame.
"He was a tremendous guy, everyone loved him," said Tommy Lasorda, who roomed with Zimmer in the Minor Leagues and played with him on the Brooklyn Dodgers. "Rooming with him was unbelievable.
"He was funny. He was dedicated. He loved the game of baseball. You couldn't duplicate him," said Lasorda.
"He made people happy from the East Coast to the West Coast," said Leyland. "He was one of the most popular people in baseball for a long time. He was a character. This guy was a fan favorite everywhere.
"With Zimmer, it was family first, baseball second and horse racing third," added Leyland, who shared Zimmer's love of racing and frequently went to the track with him, wherever they might be.
"It's kind of ironic that we are honoring his memory on the day of Belmont. I once told Zim, 'You're a Triple Crown winner.' You played baseball in the Major Leagues, you managed in the Major Leagues and you coached in the Major Leagues."
"When someone you love passes away, it's always tough," said Rays manager Joe Maddon, who stopped outside Zimmer's beloved St. Petersburg dog track, Derby Lane, to snap a photo on his way to the ballpark Saturday morning. "You grieve, but you celebrate at the same time."
"I look at it as a celebration of a great man's life," said Rays pitcher Chris Archer, who loved listening to Zimmer talk about his Dodgers teammate Jackie Robinson.
"Jackie was an awesome dude and Zim was one of his main guys. That's absolutely awesome. [Zimmer's] knowledge of this game and his character [were] timeless.
"He's a happy man; he's in a good place," Archer added. "I'm happy I was able to cross paths with such a good man."
In memory of Zimmer, Torre wore a necktie covered with images of horses. But Zimmer hated neckties.
"It would have been better if it had been a clip-on," Torre admitted.
In fact, Torre loosened his tie as soon as the ceremony started, when Rays TV broadcaster Dewayne Staats asked everyone in attendance to remove their ties in honor of Zimmer.
Zimmer's granddaughter, Whitney Goldstein, threw out the first pitch to Tom Zimmer, Don's son, who is a scout for the San Francisco Giants. Both wore Zimmer's Brooklyn Dodgers uniform No. 23.
The video presentation on the scoreboard Saturday brought a standing ovation from the Tropicana Field crowd. The Rays and Mariners wore throwback Brooklyn Dodgers uniforms from the 1950s during the pregame ceremony.
The Rays have set up electronic billboards around the bay area to display Zimmer's picture. His Rays jersey with his name and his No. 66 on the back was conspicuously hanging from the ceiling in the clubhouse Saturday.
Zimmer died on Wednesday at age 83. In accordance with his wishes, there will not be a formal funeral.
The family has asked that, in lieu of flowers, donations be made to the National Kidney Foundation (kidney.org) or the Baseball Assistance Team (baseballassistanceteam.com).