In Mariano Rivera's playing days, he believed, as a general rule, that you shouldn't fraternize with opposing hitters. At All-Star Games, he was polite to his temporary teammates, especially the pitchers, but he wasn't really into hanging out with the sluggers.
Rivera believed you should keep your emotions locked down in success or failure. When you won, you should act like it was the expected result, and if you lost, you should never, ever allow an opponent to think they had accomplished more than just winning that day's game.
As the Diamondbacks swarmed the field to celebrate Luis Gonzalez's series-winning bloop single in Game 7 of the 2001 World Series, Rivera walked off the field at the same pace as in those hundreds of instances he clinched a save and moved to the catcher to exchange a handshake.