The former England captain conceded that the power of players has grown exponentially since he retired in 2006, but there still can be 'no excuse' for any player to refuse to warm up or go on as a substitute for their team.
City have been thrown into turmoil following a dramatic and very public bust-up between Mancini and Tevez with the Italian accusing his striker of refusing to come on as a sub during their 2-0 defeat to Bayern Munich on Tuesday.
Tevez has rejected the claims although the club have already moved to take action against the Argentinean by suspending him for two weeks. The ban seems almost certain to be the start of a drawn-out disciplinary process which could end a stormy two-year period for Tevez with the club.
"I think it's probably important for him, and for football, that the owners back Mancini," Shearer told the Daily Mirror.
"I'm sure they will. In a way, they have backed him with the two-week suspension for Tevez.
"That buys everyone a little bit of time to see what they can or can't do. They have to back him [Mancini]. Because if they don't, there's no future for Mancini.
"Mancini might be restricted in what he can actually do to him. But that's the situation that managers are in now.
"You're sat on a £40million investment who's on god knows how much a week. Wherever he goes, he's not getting that anywhere else. What do you do?
"There's one club in the world that can discard him because of the wealth that they have - Man City."
Shearer revealed he understands the frustration Tevez - who was City's best player and skipper last season - must have felt to no longer be in the manager's first team plans but believes he should have handled it better.
Shearer was famously dropped to the Newcastle bench by manager Ruud Gullit for a derby game against Sunderland in 1999. He did come on as a substitute but Newcastle still lost the game and Gullit was sacked soon after that.
"Yeah, but I was put on the bench and I went on," Shearer said.
"I understand the frustration and the anger that players feel when they are left out because, yeah, it could get personal.
"But you're still employed, you're still getting paid, you've still got to go out and do whatever.
He added: "It was a different situation for me. Gullit put in an 18-year-old [Paul Robinson] kid who had never played and [had] never scored in the reserves, whereas Mancini is playing people like Aguero and Dzeko, who cost £30m or £40m.
"But I was on the bench and I was asked to go on and I did."
However, Tevez has found some friends in familiar faces. Former Manchester United midfielder Paul Scholes has backed his ex-team-mate over his apparent refusal to warm up that has caused such a furore in world football.