Mariano Rivera Reveals How Derek Jeter and Andy Pettitte Made His Last Day as a Yankee 'Magical' (Exclusive)

"That memory is like a stamp on my brain," the MLB legend recalls to PEOPLE exclusively of his final moment on the mound after his 19 season-career as a Yankee

Mariano Rivera hung up his Yankee jersey over a decade ago, but he remembers his last day in pinstripes like it was yesterday.

The professional baseball pitcher reminisced with PEOPLE exclusively about his final moments on the mound in 2013, while sharing what made it so emotionally special after his illustrious 19-season career with the New York team.

"That memory is like a stamp on my brain," Rivera — who solidified his name as one of the greatest closers of all time — tells PEOPLE in an exclusive interview from the stands behind home plate at Yankee Stadium on Tuesday, July 30.

The retired player, 54, made his last appearance for the Yankees on Sept. 26. Per manager Joe Girardi's request, Rivera was greeted at the mound by teammates Derek Jeter and Andy Pettitte to take the ball from him in a tear-jerking surprise that had 48,675 fans cheering from above.

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"It was such a great moment that it was just magical," Rivera says of the moving gesture. "It was a blessing to have Derek and Andy pulling me out of the game from that stage like that... I'm telling you, it was just amazing."

Rivera, Jeter, 50, and Pettitte, 52, are three players who make up the famed Yankees "Core Four," along with retired catcher Jorge Posada. Each member was a key contributor to the team's dynasty that won four World Series titles in five years during the late 1990s and early 2000s.

Although Pettitte and Jeter retired in 2011 and 2014, respectively, Rivera still shares a unique connection with his baseball brothers to this day. "It's a bond. It always will be," he tells PEOPLE.

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"It is good," he continues of their relationship. "I talk to them once in a while. Andy is in Texas. Derek is in Miami and we still chill. I just saw him last week in Cooperstown and we shared a little bit there, so it's good."

Despite not spending time like they used to when they were teammates, each stepping away from the game professionally and moving outside the New York area that they called home for so many years, Rivera made one thing clear.

"You're always a Yankee... It's in the family," he says with a smile.

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"We've been able to do it for so many years and do it here in New York," Rivera continues. "I was grateful to the Lord that allows me to do the job day in and day out for so many years. I enjoyed it. Whatever the outcome was, I enjoyed it."

While the Yanks mentality is there for Rivera, the 13-time All-Star has put the physical side of it to rest. "I don't do none of that stuff," he says of pitching baseballs in any capacity today.

"This is the first time that I have done it in years," Rivera reveals in reference to throwing the ball at the batting practice event hosted by Poland Springs — the official water of the New York Yankees — on Tuesday. "This will be my 11th year retired, so since then."

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Despite retirement, Rivera's still got it! "I feels great. It feels amazing," he says of getting back in the batting cages nearly a decade later. "Even just throwing the ball, feeling the hitters and all that stuff... It was great."

As for how his shoulder feels after a career that solidified his name in the MLB Hall of Fame? "It feels good," he says. "Especially again, you drink, you hydrate yourself with Poland Spring... It feels the greatest."

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