Uruguay beat Argentina for the first time since 2013 after goals from Barcelona's Ronald Araujo and Liverpool's Darwin Nunez proved enough to secure a 2-0 victory in Buenos Aires on Thursday evening.
The result ended Argentina's 14-game unbeaten run, while it also represented their first home defeat in World Cup qualifying since October 2016.
The fiery contest saw Paris Saint-Germain midfielder Manuel Ugarte make an obscene gesture towards Rodrigo De Paul, which ultimately drew an angry reaction from the Atletico Madrid man.
The tempers also flared when Messi was seen putting his hands on the throat of Mathias Olivera after he had clashed with De Paul.
Following the defeat, the eight-time Ballon d'Or winner criticised the young Uruguay players for showing a lack of respect.
Messi told reporters: "These kinds of games, qualifiers, against Uruguay, it's always like that. I prefer not to say what I think.
"Young people have to learn to respect their elders. These games are always intense but very respectful, so they have to learn a little.
Despite being frustrated by some of the conduct from Argentina's opponents, Messi did offer praise for his compatriot Marcelo Bielsa, who has overseen five victories in his first seven games in charge of Uruguay.
"You can see Bielsa's hand on the way Uruguay is playing. In all the national teams or clubs, including Argentina, his style was very recognizable. And he has a good generation of players.
"They are an intense team and it was difficult for us to play our game. They have physical and fast players in the midfield.
"We never feel comfortable and we didn't find a way to possess the ball for a long period of time. So the game was played on a fast pace and we fall for that style, which isn't the best for us."
Having beaten Brazil and Argentina in their last two matches, second-placed Uruguay are just two points behind the world champions, who still lead the South American qualifying group.
Argentina will now turn their attention to Tuesday's meeting with their rivals Brazil, while Uruguay will play host to Bolivia.