Brazil claimed its first Copa title since 2007 with a 3-1 win over Peru in the final at the Maracana.
However, there have been suggestions Tite is considering moving on despite being contracted until 2022.
Alves, who was named the best player of the 2019 Copa America, lauded the impact of the 58-year-old.
"The captain of our boat is Tite," he said.
"Congratulations to us and to our people. I repeat, congratulations to our staff."
Alves said: "Playing in the Maracana is always very special. It is our house."
While Everton's opener was cancelled out by a Paolo Guerrero penalty, Gabriel Jesus' goal and Richarlison's late spot-kick gave Brazil a ninth South American title despite the Manchester City forward's red card.