Given time off while other players are on international duty, Tevez came home to Buenos Aires for a break as he was not called up to the Argentina team on a tour of Asia that included Friday's 1-0 win over Venezuela in a friendly in India.
"We had clashes with Mancini in every language but it's a love-hate relationship," Tevez was quoted as telling reporters on arrival at Ezeiza international airport.
"He's fantastic, he wants to win and me too. He told me to come to Buenos Aires to enjoy a holiday. He left me out of these first few [Premier League] matches because I told him I needed to get in shape," said the 27-year-old.
"I'm happy at City and I'm not moving from there," added Tevez, who during the Copa America, where he turned out for Argentina, had issued a statement saying he wanted to leave the club. He had said several times he did not like living in Manchester, nor did his family.
Tevez complained he had been a scapegoat for hosts Argentina's quarter-final elimination by Uruguay in the Copa America after missing a penalty in the shootout with the tournament's eventual winners.
"To play in the national team today you can lose prestige because if you don't win they kill you," said Tevez of criticism in the Argentine media.
"We were under pressure to win because that was the only possible result [at home], if not... we knew they'd kill us. I got depressed and ate after being unable to give the [Argentine] people happiness," he said, adding that he put on six kilos and had to go to a clinic to lose weight.
"It hurts a lot not to be able to play the way you would like."
Argentina's poor form led to the sacking of coach Sergio Batista, who decided only at the last minute to include Tevez in his squad after public clamour for the man dubbed "the people's player".
Tevez started Argentina's first two matches, both draws, but his form was poor. He came on as a substitute against Uruguay.
