Tevez had been heavily tipped to quit City this summer after reportedly becoming disenchanted with life under his new boss.
However, Mancini met the Argentina star in midweek and was assured that he wants to stay at the club despite their failure to secure a place in next season's Champions League.
"I have spoken with Carlos and asked him whether he was happy to stay here," revealed Mancini. "He said he was very happy, that he wanted to improve and wanted to win with Manchester City. This is important.
"Carlos is a top player. He can set the example for the others."
Tevez collected City's player of the year award on Thursday night, a fitting accolade after a season that had been full of highs until he recently complained about Mancini's preference for double training sessions.
"I have told him that in any week where we don't have a midweek match on one day we must have two training sessions," added Mancini.
"Because we have qualified for the Europa League, the chances are we will be playing nearly every Thursday and Sunday.
"But if we want to improve we must work harder than this year."
Mancini's own future was confirmed by chairman Khaldoon al-Mubarak in his statement to the club's website on Thursday afternoon.
Not that the City chief needed any clarification. He already knew a statement he came out with on the day he was unveiled last December had been misinterpreted.
"What Khaldoon said was important," he said. "When I first came I said my contract was six months, plus three years. People thought I said six months and (only) if I finished fourth would I stay for another three years."
Mancini will sit down for a full season debrief with chief executive Garry Cook and football director Brian Marwood next week to thrash out plans for next season.
Funds will be placed at the Italian's disposal to strengthen in the areas he feels City fell short this year as they try to improve on what could end up being a fifth-placed finish.