The Argentina international, who left the Premier League runner-up for Italy this summer, thinks the club and its fans need to be more patient for success in Europe.
The 29-year-old ended his stay at the Etihad Stadium this summer, joining Serie A champion Juventus in June for a fee of around 12 million euros.
City failed to progress out of the group stages of the Champions League in consecutive seasons and Tevez believes pressure played it's part.
"Yes, there was way too much pressure,” Tevez told CNN. "It came from everyone - the club, the fans. I think that too much pressure just hurts the team.
"What happened was that there was so much hype and pressure to be one of the giants of Europe and we didn't do it. We dropped out in the first round of the Champions League on both occasions."
Tevez, who failed to register a goal in Europe last season, despite netting 11 times and assisting eight goals for City in the Premier League, moved to Turin on a three-year deal.