Messi had earlier made comments in which he appeared to accuse the South American Football Confederation (CONMEBOL) of corruption and raised questions about the manner in which Brazil had reached the tournament's final, reports Efe news.
"Here, I considered him an extraordinary player, extraterrestrial, but he needs to have a little more respect and understand and accept when he is beaten," Tite said during the post-match press conference after Brazil won the final against Peru 3-1 on Sunday.
"We were wronged in several matches here and in the World Cup. Be careful with what you say, because each one has his own situation," Tite added.
After the match for the third place, in which Argentina beat Chile 2-1 and in which Messi saw a red card in the first half the FC Barcelona legend lashed out against CONMEBOL.
"I didn't go to the award ceremony because of a little bit of everything. I think we don't need to be a part of that corruption, of the lack of respect we faced during this Copa," Messi had said after the game.
"I'm leaving with the sense that they didn't let us be in the final, that we could've done more," he added, alluding to the referee's refusal in the semifinal against Brazil to use the Video Assistant Referee system to review two possible penalties claimed by Argentina.
The Argentina captain implied that Brazil had a great influence over CONMEBOL after his team's elimination in the semifinal by the host country.
In this regard, Tite responded saying he wanted to make it clear that in that game, Messi had suffered only three fouls and that Brazil had played a clean game.
The Brazilian coach, however, said that he could understand his outburst following his unfair expulsion in the match against Chile.
Messi's comments had also drawn the ire of CONMEBOL, which on Saturday released a statement criticising the Argentina forward.
"It is unacceptable that, following individual incidents in the competition, where 12 teams took part, all in equal conditions, unfounded accusations have been made that are lacking in truth and call into question the integrity of the Copa America," read the CONMEBOL's statement.
"In soccer, sometimes one wins and sometimes one loses, and a fundamental pillar of fair play is to accept the results with loyalty and respect. The same goes for the decisions made the referees, who are human and will always be perfectible," it added.
The Copa America exit at the semi finals marked the end of the 2018-19 season for Messi, who is still looking to earn his maiden title with Argentina after having won virtually everything during his unparalleled club career.
( With inputs from IANS )