Augusto has been a mainstay in Brazil's starting lineup since 2015 and has shrugged off concerns that his move to China in January last year might impact his international career, reports Xinhua news agency.
"I'm very grateful to Dunga because when I went to China he supported me," Renato told reporters on Sunday.
Dunga was sacked as coach in June after Brazil's group-phase elimination from the Copa America in the United States.
But his replacement, Tite, has since led the Selecao to six straight victories and they now lead the South American zone qualifying standings for the 2018 World Cup in Russia.
A victory against Uruguay in Montevideo on Thursday or against Paraguay in Sao Paulo five days later will secure the team a place in football's showpiece tournament.
"I thought that things would take longer under Tite," Renato said.
"But he pays a lot of attention to detail and the team has benefited a lot from that."
Unlike Brazil's Europe-based players, Renato and Guangzhou Evergrande midfielder Paulinho have had to embark on their own training regimes to be fit for the qualifiers.
"I have prepared a little differently compared to other matches because, unlike the players in Europe, I have been on holidays," Renato said.