"Things weren't looking very good," Cox said when asked recently to reminisce about those years.
But it's safe to say Cox's view was grand this past weekend when he was inducted into Baseball's Hall of Fame with two of the prized pitchers -- Glavine and Greg Maddux -- who made his managerial days in Atlanta so special.
The inductions led thousands of Braves fans to flock to Cooperstown to celebrate these careers and the unprecedented era these men helped create in Atlanta. Glavine and Maddux were together for 10 of Cox's division titles.
Cox certainly recognized and appreciated the unique honor of being inducted at the same time as two of his players.
"I think the odds of hitting the lottery would be better than this ever happening again," Cox said. "It's pretty darn special. I like the way [the Hall of Fame] laid it out [on Sunday]. I got to go [speak] between Greg and Tommy, which I thought was really neat."
Cox, Maddux and Glavine all took time during their speeches to recognize John Smoltz, their longtime Braves teammate who will become eligible for the Hall of Fame next year. Cox also said he is looking forward to the day when he returns to Cooperstown for the inductions of team president John Schuerholz and Chipper Jones, who will become eligible in 2018.
"Chipper, you'll be standing here soon, and thank you for everything you've done for the Braves organization," Cox said during Sunday's speech. "Thanks to all the players, coaches, scouts, trainers, clubbies and front-office personnel that passed through Atlanta and helped make the Braves organization what it is today."
Legendary scout Paul Snyder, who served as Cox's right-hand man during the club's rebuilding process in the late 1980s, was present on Sunday. As was the team's current scouting director Tony DeMacio, whose first signee was Glavine.
Former Braves coach and current Dodgers scout Pat Corrales began making arrangements for this trip in December, when he learned about the induction of Cox, who he first met as a teenager. Corrales shared the celebration with his current boss Stan Kasten, whose role as the Dodgers' CEO and president is similar to the one he held with the Braves during their glory days.
Schuerholz also invited his longtime right-hand man Dean Taylor, who serves as the Royals' assistant general manager.
"John Schuerholz should be popping buttons everywhere," Cox said. "He hired us on and signed everybody. He's got to be proud of that."
Like the fans, this weekend's ceremonies gave the honorees a chance to truly appreciate this era.
"I think when you see a lot of that stuff and you start to really process it, it really sinks in that we had some good teams," Glavine said. "We had some good players who were around us. I think it made me appreciate all of that more so than I ever did as a player, because you're so locked in, you don't take the time to think about what you're doing sometimes."
When Hank Aaron was introduced before Sunday afternoon's induction ceremonies, a crowd of more approximately 48,000 roared, leading emcee Gary Thorne to say, "Hank, I think Atlanta is here."
Whether from Atlanta or some land where TBS once brought the gift of baseball on a nightly basis, Braves fans crowded the Cooperstown streets in abundance this past weekend. Dale Murphy may never get into the Hall, but he was certainly treated like an inductee by the many fans who found him signing autographs on Main Street, just a few doors away from the Hall of Fame.
Murphy was just happy to be present to celebrate with Glavine, a player he helped mold during the late 1980s, and his first manager, Cox, whose patience and optimism helped the two-time NL Most Valuable Player Award winner make the transition from catcher to outfielder.
"[Cox] saved my career," Murphy said. "He saw there was something in there."
What Cox saw this past weekend was more than he could have ever imagined when he first met Glavine nearly 30 years ago. But together, they both had reason to feel a sense of pride that will be extended when they return within the next few years to celebrate the inductions of Smoltz, Jones and Schuerholz.
"It was a pretty good run of success, and there were some pretty special guys who were a part of it," Glavine said. "Considering where we were able to take the Braves organization from and then to in the baseball world, it was pretty special to be a part of all of that. The three of us going in signifies what we were able to accomplish as a team and as individuals. There were will be a couple more guys going in soon."