Gregg Popovich spoke at length for the first time since his recent medical emergency ... saying he's getting better every day, but not fast enough to continue leading the San Antonio Spurs.

The five-time NBA Finals-winning coach took the podium before Mitch Johnson was introduced as his official replacement on Monday ... and had his two longtime players, Manu Ginobili and Tim Duncan, by his side.

76-year-old Pop -- who suffered a mild stroke in November and another health scare at a local restaurant last month -- spent the majority of his time thanking those who assisted him over his nearly 30-year tenure on the bench.

He also addressed how he's doing since the stroke ... claiming "things are getting better by the day, but it's not good enough for what we plan ahead," so a change in leadership was necessary.

He did not go into detail on his dinner that resulted in a trip to the hospital.

Pop mentioned everyone in the organization -- former players, coaches, ticket salespeople, in-game entertainers and more during his speech ... saying, "We all have a part in this."

Pop also noted the folks who have helped him with rehab -- and some were even present for the event.

When discussing his successor, Popovich said Johnson is fully capable of giving 100% every single day ... which the team needs at this time.

He also praised Johnson for the job he did in his absence this season ... which he admitted were difficult circumstances to be thrown into.

As for his new role as team president, Pop made it clear he's in a lighthearted mood over it all ... taking off his track jacket to reveal a shirt that read "El Jefe" and "Señor Popovich, President of Basketball Ops."