Tevez, who signing a five-year contract with City following a two-year loan spell at rivals United, said the Spanish giants had been interested in recruiting him but Eastlands proved preferable to the Bernabeu.
"Real made an offer but there was no agreement," the Argentina striker told the Nation newspaper during a promotional visit to Abu Dhabi with City.
"There were talks about deals and agreements but in the end it was only City. They showed lots of interest in me and are intent on growing and signing big players.
"I am sad to leave United but I am excited to join City. I'm thinking about the future and I will grow with this club."
Meanwhile, City owner Sheikh Mansour has constructed a multimillion-pound warm-weather training facility in Abu Dhabi so that his club can enjoy a winter break in the sun.
Their first visit is set for November 12 to play against the United Arab Emirates national team.
Meanwhile, Gareth Barry has hit back at accusations his move to City was motivated by money and claimed the club's recent acquisitions have justified his decision.
Barry left Aston Villa to join City in a £12m switch at the start of last month after snubbing long-standing interest from Liverpool.
Reds boss Rafael Benitez criticised the decision, suggesting it was taken due to "money, money, money".
But England midfielder Barry claims the recent signings of Roque Santa Cruz and Carlos Tevez prove he was right to move to Eastlands.
"I think there was maybe a bit of frustration (from Benitez) because it was well documented that Liverpool were in the market to sign me for a couple of years," he said on Friday.
"But Manchester City had agreed a fee with Aston Villa.
"Once I'd spoken to the manager, heard the ambition and he told me what the club were aiming for, that suited me.
"People can talk about the money because of the speculation in the media but the players that are now joining are proving my decision to be a correct one.
"These are players that are really going to improve Manchester City and take us to where we want to go."
Barry was speaking on City's pre-season tour of South Africa with the first game coming on Saturday afternoon against the Orlando Pirates.
He added: "I think all the players are delighted to be here in South Africa.
"We've just come back from holidays and we're mainly focusing on fitness over here.
"We see the two games against the big clubs over here as part of building up towards the start of the Premier League.
"We know the standard of the football here is very high, so we'll be having a big test and as I said, building towards the start of our own league."