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."