I would not tell him to stop being excited about his performance, or stop showing your own excitement at his successes. I would, however, not treat every home run he hits or every catch he makes as if it was the game-winning hit or catch in the last game of the World Series. If you always remember to focus on his efforts rather than his big achievements, then you send him a message that you appreciate his efforts and the fact that he's having a good time more than you value his home runs. If you communicate to him that you are excited or pleased with him only when he "succeeds" in a big way, then he'll doubt himself if he doesn't always acheive the same level of performance.
In talking about the game with him afterwards, I would make a point of commenting upon his developing skills ("Boy, you're definitely running faster around the bases these days." "You're really looking right at the ball when it hits the bat.") while still noting his pleasure about his home runs, etc. I'd also make it a regular after-game ritual to ask him to comment upon which teammates did a good job (as well as opposing players), who was improving, and who was a supportive teammate. I would always reinforce your appreciation of his sportsmanship and support of his teammates.
You can model this type of thought process and behavior in your everyday lives by making sure that you focus on peoples' efforts and not just their "home runs." Your boy will grow up knowing that you'll always offer him encouraging words, appreciating his efforts and his enthusiasm for whatever he attempts. He'll know that whether he strikes out with three runners on base, or whether he hits a grand slam to win the game, that you will honor who he is.