Tevez will not captain City
Tevez, as skipper, was inspirational last season and lifted City's first trophy in 35 years after victory in the FA Cup final. The Argentina forward, however, was unsettled off the field and expressed a desire to move closer to his family in South America.
But after a proposed move to Brazilian club Corinthians collapsed and no other clubs made firm offers, Tevez was forced to return to City.
The 27-year-old is yet to start a game this season and Mancini feels the influential Kompany, 25, who has been leading the team instead, should fully inherit the captaincy.
Mancini said: "The captain is Vinny Kompany. The reason is simple. Carlos in the summer wanted to leave the club for family reasons.
"I respected his opinion to leave the club. But Carlos is here now, we didn't find any solution for him. He is a fantastic player for us because he can score 20 goals in one year - but I decided in the summer Vinny was the captain."
Delighted with Dzeko
Tevez has been City's top scorer for the past two seasons but now appears to be behind Edin Dzeko and record signing Sergio Aguero in the pecking order.
Dzeko, who struggled to make an impact in the second half of last season after his £27million arrival from Wolfsburg in January, has been in particularly good form.
The 25-year-old Bosnian has scored seven times in four appearances this term, including one in the FA Community Shield and four against Tottenham Hotspur.
Mancini said: "Edin is a fantastic striker, he scores everywhere. I am sure that this year Edin can score a lot of goals for us."