Not everyone has the clutch gene -- and MLB playoffs legend Curt Schilling says that includes Clayton Kershaw, who exposed himself in this year's World Series.

We spoke to Curt about big-game pitching after the Dodgers' W.S. collapse ... and he didn't sugarcoat what separates guys like him from the Kershaws of the world -- Hall of Fame talents that don't show up when the lights are brightest.

"You have to want to be in a situation where everything's on you," Schill told TMZ Sports.