Puig, who has been criticized throughout his rookie season for his emotional style of play, celebrated twice on his RBI triple that helped the Los Angeles Dodgers beat the St. Louis Cardinals 3-0 on Monday night.
Beltran, the Cardinals' All-Star right fielder, clearly was annoyed by Puig's antics.
"As a player, I just think he doesn't know [how to act]," Beltran said. "That's what I think. He really doesn't know. He must think that he's still playing somewhere else.
"He has a lot of passion, no doubt about that -- great ability, great talent. I think with time he'll learn that you've got to act with a little bit more calm."
Immediately after belting a long drive to right field in the fourth inning, Puig raised his arms and stood in the batter's box to watch the flight of the ball, clearly thinking it was going out of the park.
But once he realized it wasn't, Puig started charging around the bases and roared into third, clapping his hands before raising them again as the sellout crowd of 53,940 cheered.
"I'm in the outfield," Beltran said. "I mean, it's not great. To me, I don't like it. But what can I say? I don't play for them. I just play over here. I just need to do my job. It is what it is."
Dodgers outfielder Carl Crawford defended Puig, saying the 22-year-old Cuban energized the Dodger Stadium crowd.
"It's Puig, man," Crawford said. "He's been doing it all year. I mean, I know it's one of those things where a rookie probably shouldn't be doing that kind of stuff. But they love it around here. So I guess it's OK."
Dodgers outfielder Jerry Hairston Jr. says Puig does not intend to disrespect opposing teams.
"I know, with his exuberance, sometimes the opposing team might not like it," Hairston said. "But they've just got to understand, he doesn't mean anything by it. He just wants to do well.
"I totally understand the opposite side and their view of it. But what I would say to them is, you've got to remember, this guy is like a 16-year-old kid playing Little League. He's just so passionate, so emotional about the game. He really means no disrespect. He really means no harm. He just got excited tonight. He got a really big hit for us."
But Beltran warned that Puig's celebrations might ultimately galvanize the Cardinals, who enter Tuesday's Game 4 with a 2-1 series lead.
"When you try to do those things sometimes, you know, you get that attention," Beltran said. "And you don't want to wake up nobody. I always thought if you hit a home run off a pitcher, you've got to make him believe he made a mistake. You don't wake him up. Or next time, the pitcher's going to be more focused with you and he's going to try harder to get you out.
"So he will learn. I don't think he's a bad kid. I just think he doesn't know right now."
Information from ESPN.com's Jayson Stark and The Associated Press was used in this report.