Having seen Argentina lose to Brazil in the semi-finals, before being sent off against Chile in a third-placed play-off, Messi suggested the officials have been favouring the tournament hosts throughout.
Brazil ultimately did claim their first Copa America since 2007 after beating Peru 3-1 in the final with their coach declaring Messi was wrong to cast any doubt over their triumph.
"The one I treated as extraordinary, as extraterrestrial, needs to have more respect and accept when he is beaten," Tite said of Messi post-match.
"We were harmed [by referees] in several games. We played fair against Argentina the whole time.
"I am being honest. He put huge pressure [on] because of his reputation."
While unhappy with Messi's conduct, Tite did concede the Argentine captain shouldn't have been sent off against Chile.
The 32-year-old was involved in a physical exchange with Gary Medel in the first-half with both show straight red cards.
"He was expelled in an unfair way. It was Medel," Tite said. "For him, it was a yellow card, at max."
Brazil midfielder Casemiro was also asked about Messi but played down the Argentine’s comments.
"Those who have a mouth speak what they want," the midfielder told reporters.
"It's not my turn to speak. It's a delicate issue.
After guiding Brazil to silverware on home soil, Tite is the first manager ever to win the Copa America, the Copa Libertadores and the Copa Sudamericana.
Dani Alves, who was voted player of the tournament, was full of praise for the Selecao coach.
"The captain of our boat is Tite," Alves said. "Congratulations to us and to our people. I repeat, congratulations to our staff .
"Playing in the Maracana is always very special. It is our house."
Alves also spoke up on Messi, telling reporters: "I don't agree with what Messi said, we have worked hard to be champions.
"We sweat a lot. I can understand that Messi is upset, but I don't agree that it was set up because we sweat a lot to get this."
Messi meanwhile had another tournament to forget with Argentina with CONMEBOL also claiming his accusations of favouritism lacked respect .
The Barcelona legend refused to accept his third-place medal on Saturday as he declared the Copa America was corrupt.