"When I was with the Yankees, and we won the world championship, and you wear the pinstripes, you think you're pretty cool," the 41-year-old athlete recounted. "But then, you hang out with Jennifer, and they confuse me with the security guard all the time!"
The former All-Star said that he even gets sidelined by paparazzi when he and Lopez hit star-studded red carpets at black-tie galas.
"We were at the Met Ball, and the paparazzi were screaming at me, not even in English, 'Get the hell out of the way, get out of the way! We're trying to take a picture!'" Rodriguez recalled.
"I love the game so much and honestly, it's too much," he joked. "I have three televisions in my living room and I'll have the east coast game, the central game, and the west coast game and my daughters are like, 'Daddy it's too much, I thought you were retired!'"
Rodriguez and Fallon also played a game of "Egg Russian Roulette" -- while decked out in Yankee pinstripes -- and went head-to-head smashing eggs (decorated like baseballs) onto their foreheads without knowing if they're hard-boiled or raw.