The 29-year-old completed his move to Turin on Wednesday for a fee beginning at £10 million, a transfer which brings to an end his four-year spell at the Etihad Stadium.
Tevez played a major role in City's rise to the top of English football in recent seasons, helping them to win the FA Cup in 2011 and the Premier League title in 2011-12.
"It will be a massive loss for Manchester City," Barry told Sky Sports.
"He has had a fantastic few years there and he has been fantastic to play alongside. To hear that news is quite sad but he will go and do a great job wherever he goes."
Tevez is City's top scorer in the Premier League era with 58 goals.
Source: Manchester City MAD