Pedro Martinez is happy to be part of “the fun times” of Boston sports history.

On Saturday, Martinez, 51, attended the world premiere of David Duchovny‘s new movie Bucky F—ing Dent at the 2023 Tribeca Film Festival, where he caught up with PEOPLE about his memories of baseball’s iconic rivalry between the Boston Red Sox and New York Yankees during his seven MLB seasons pitching for Boston.

Duchovny’s new movie follows a Red Sox-obsessed father and his estranged son during the 1978 MLB season, which ended with a Yankees victory over the Red Sox in a one-game, win-or-go-home playoff game. The big hit in that game for the Yankees was a three-run home run by light-hitting shortstop Bucky Dent — which earned him an expletive-punctuated nickname among Red Sox fans.

The game took place long before Martinez joined the Red Sox in 1998, but the Hall of Famer is well aware of the team’s painful history.

“The long years of suffering. Heart breakers,” he tells PEOPLE when asked what first comes to mind when he looks back at his years in the heat of the Red Sox-Yankees rivalry. The Red Sox famously did not win a World Series between the years 1918 and 2004; the Yankees won 26 in that 86-year timeframe.

“It also comes to my mind every time I see [that 1978] series, when they have their hearts broken, it made me realize that I was [up] against probably a tougher challenge than I ever imagined,” Martinez, who played a key role on the 2004 Red Sox team that beat New York on its way to a World Series victory, tells PEOPLE. “Because I stopped to look at the people that were playing on that [1978] team, and the reason it hurt more is because the teams were equally as good, and maybe we were better [than the Yankees].”

“And we happened to lose that game, that way, and lose the series,” the former MLB pitcher continues. “Looking at the stars that were in the team, the great players that went through, it’s hard to imagine that they never got a championship in Boston.”

“For me, today, representing Boston — to be here, and know that I was part of the first [Red Sox team] that won [the World Series in decades] it gives me great joy, satisfaction,” Martinez adds. “I’m representing the fun times. Not so much the hurting times.”

After 1978, Boston’s baseball fans went on to have their championship dreams crushed multiple times more before winning the World Series in 2004, including a Game 7 playoff loss to New York in 2003 in which Martinez gave up the lead late in the game.

“Even I had my heart broken” by that game, he says.

Now, Martinez works as an analyst at the MLB Network and MLB on TBS.

“Baseball’s faster, younger,” Martinez says. “Some of the [rules] they changed, I think I agree with most of them. I’m extremely happy with the way things are actually looking.”

“The fans are coming back to the stadium. You see a lot of fans in the stadium,” he adds. “They can stay there for two, two and a half hours and go to dinner. I think it’s great. Baseball is striving the right way.”