Tevez's stint at City - ended by his transfer to Juventus this summer - lasted four years, during which the big-spending Blues won the FA Cup and Barclays Premier League, but were also eliminated at the group stage of their maiden Champions League campaign in 2011-12 and suffered the same fate in the competition last season.
Regarding the weight of expectation that was on the City team in terms of Europe, the Argentina forward told CNN: "Yes, there was way too much pressure.
"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."
Overseeing the trophy triumphs and the disappointments in Europe was Roberto Mancini, the Italian who lost his job as City manager when he was sacked in May and has been replaced by Manuel Pellegrini.
The relationship between Mancini and Tevez certainly had its ups and downs, with a particular flashpoint being the player's refusal to warm up during a Champions League game against Bayern Munich in 2011.
Tevez, 29, has spoken respectfully about his former boss, though, saying of Mancini: "He's a winner.
"I think he's a winner because he always wants to win and he takes his team to the maximum place to be able to win.
"Everyone who knows Mancini knows that he's a winner from birth."
Source: Manchester City MAD