Tite claimed that Messi told him to “shut his mouth” after protestations from the Brazil who wanted the superstar booked for a challenge.
Messi netted the only goal of the game in the 13th minute when he converted a rebound after his penalty was saved by Brazil’s Liverpool keeper Alisson.
Brazil forward Gabriel Jesus had earlier missed a spotkick, having failed to convert for Manchester City against Atalanta Bergamo last week too.
Speaking about the incident with Messi, Tite said: “I complained because he should have been shown a yellow card and he told me to shut my mouth and I told him to shut his mouth. That was it.”
He added: “I don’t want to answer anymore on it. You need a strong referee because he’ll swallow you… It should have been a card, I was right to complain.”
The Brazil boss was visibly complaining over the incident, with Messi put his hand over his mouth when he uttered the alleged remarks.
Tite acknowledged that Messi was impressive in the Argentina win, upon his return to international football after a four-game ban.
Argentina boss Lionel Scaloni said: “I liked the second half. We made changes because we wanted to prepare for the tests that are coming.
“The team responded and played really well.”
Argentina will take on South American rivals Uruguay in a friendly next week while Brazil next meets South Korea in Abu Dhabi.