Van Persie, whose form had been questioned ahead of Sunday's Barclays Premier League clash at Old Trafford, secured a 1-1 draw for his side by slamming home in the 94th minute.
Lost in the euphoria of the moment, he promptly whipped off his shirt and flung it in the air in celebration - earning a booking from referee Phil Dowd and a ticking off from Van Gaal.
"He did a stupid reaction after the goal," Van Gaal said.
"You can be excited but you don't have to pull your shirt off because then you have a yellow card. It is not so smart."
Van Gaal's counterpart Jose Mourinho was also unhappy post-match with someone in particular - Dowd.
That much was clear, despite the Chelsea manager insisting he had no comment to make about the official as he did his best to avoid getting into trouble with the Football Association.
The visitors had a penalty appeal turned down in the first half when Chris Smalling tussled with Branislav Ivanovic.
Then, after Didier Drogba's 53rd-minute header had put Chelsea in front, they were denied victory when Ivanovic received his second booking of the game for a foul on Angel di Maria and the resulting free-kick came to Van Persie, who fired in.
Chelsea received a total of seven bookings in the game.
And asked about Dowd, Mourinho - whose team are now four points clear at the top of the Premier League - said: "You know I cannot speak.
"Some (managers) can, some don't. I am one of the ones that cannot because you know what happens to me when I speak.
"If I do (talk about Ivanovic's sending-off) I have to start in the first half and go through many things that happened.
"The (possible) penalty on Ivanovic, the accumulation of cards, the fouls not given."
He added: "To come here and play the way we did and not to be happy with the point, because we are not, shows clearly how good we were and how good we are playing at this moment.
"We are four points clear, so I can say at this moment that, next weekend, it won't matter about results - we will be top of the league.
"I prefer to be in front rather than behind, obviously, because you have a little space for your mistakes - or for the referees' mistakes."
Mourinho also stressed he regards eighth-placed United as title rivals, despite the gap between the two clubs currently standing at 10 points.
Meanwhile, Van Gaal - who felt his side "could have won" and rued the opportunities they missed despite the "fighting spirit" that saw them notch a second successive late leveller - revealed United defender Phil Jones missed Sunday's game due to shin splints.
While Jones looks set for another spell on the sidelines, there was more positive news for United regarding Radamel Falcao.
Like Jones, the Colombia striker also missed the match against Chelsea, but his injury does not look serious, which is a boost given that United travel to local rivals Manchester City on Sunday.
"Falcao took a kick in training on Thursday and couldn't play because of that," Van Gaal told MUTV after the final whistle on Sunday.
"We'll have to wait and see, but I don't think the injury is too bad. (Sunday's) match came too soon for him."