The former West Ham United forward spent two years on loan with the Red Devils, putting in strong performances as he made 99 appearances and scored 34 goals.
But following his loan spell at Old Trafford, the 27-year-old went on to join arch-rivals Manchester City and eventually win the FA Cup with them last season.
Now Sir Alex insists that it was because of the former Boca Juniors man's future plans that United decided against signing him.
"Tevez told us he was only going to play for four more years," he said. "If we had signed him on a five-year contract knowing that he was going to quit in four, there would have been no re-sale value for us."
The Argentina international has since made it clear he wants to leave City to be closer to his family in his homeland, but a potential deal with Corinthians of Brazil did not reach fruition.
Serie A giants Inter have also been linked with a move for the industrious hitman, but Sir Alex said: "I’m not sure Inter would pay £45 million, especially after he’s said he wants to go back to Argentina to see his kids. I can see him staying at City."
Sir Alex also commented on United's 3-1 friendly victory over MLS outfit Chicago Fire, in which new signing David De Gea put in a good performance."He [De Gea] is technically very good. He saved us on many different occasions," Sir Alex told reporters after the game.
"Chicago Fire played well, very good on the counter attacks, a lot of pace up front and they gave us some problems.
"They could've scored two or three more so it was a good workout for us."
The home side drew first blood when Cory Gibbs outsmarted the opposition defence, but United grew into the game and eventually put three past Frank Klopas' men.
"Well we don't like being behind," said the Scot. "We found ourselves in that situation numerous times. We don't panic, we just keep creating chances and chances until we get our result."
The equaliser came when Wayne Rooney came off the bench to make his mark on the game, and the United boss believes that the leveller changed to course of the clash.
"It was an excellent ball from [Rio] Ferdinand, perfectly awaited from Rooney and it takes serious skill to score like that," Sir Alex said.
He added: "We had to work hard for the victory and I think once we equalised, we were always going to win it."
Despite the win, the Old Trafford boss also believes that his squad are still some way from being match fit.
He said: "Well we played three games so far and I think player-wise, our players need to play 90 minutes.
"I don't think anyone has done that yet, except Ferdinand and [Nemanja] Vidic I think. It was the problem we struggled with last year at the start of the season and we need to improve on that."