The striker has made an instant impact at his new club and proved to be the match winner on Saturday evening
The pair had endured a tempestuous relationship together at Manchester City before leaving the club this summer, with Tevez enjoying a fine start to life in Italy.
"I didn’t know Mancini was in the stadium. We have kept up a good rapport," the 29-year-old told reporters after the match.
"I'm really happy here but it's not easy to slot into a new playing system, it takes time. Tonight was perfect though: a goal and a win.
"I'm pleased because it was no easy feat coming here and doing that at such a difficult ground."
Juve boss Antonio Conte then praised his new signing's work ethic and emphasised how all of his new recruits will get better in the coming weeks as they get more game time under their belts.
"A lot has been said about him but he's certainly not afraid of putting in the hard work," the Italian commented shortly after.
"I'm not happy with a striker who's static. Tevez not only offers us quality up front but he helps out defensively too.
"Tevez has scored twice already but he's also made a huge contribution to the team – that's something all my players have always done.
"The more time passes, the more comfortable Carlos, Fernando [Llorente] and Angelo [Ogbonna] will be. They're putting a lot of effort and it's not easy, but these are top players we're talking about."