The 71-year-old manager reveals that he tried to buy the young Wales international from Southampton but the Saints rejected the deal and the winger joined Spurs weeks later
The Wales international has dazzled at White Hart Lane since signing in 2007, winning the PFA Player of the Year award in 2010-11 and attracting interest from Los Blancos with nine Premier League goals from the left wing already this season.
And, while Sir Alex admits that he would have liked to bring Bale to United, he says it is simply part and parcel of the game to miss out on certain players - adding that his side are more than ready for an important clash against Spurs on Sunday afternoon.
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"It happens. You don't get them all. As I said before, we would have loved to have got [Paul] Gascoigne but we didn't - but we did get Paul Ince and he was a great player for us. These things happen."
Sir Alex has warned his United players they must beware of the pace in Tottenham's side as they look to re-establish their seven-point advantage over defending champions Manchester City. He believes that the meeting at White Hart Lane is crucial in terms of momentum in the title race.
"We know that Bale and [Aaron] Lennon have got pace, [Jermain] Defoe has pace, [Mousa] Dembele is a good footballer," the Red Devils boss added. "It is straightforward – we have to perform but it's been a good ground for us in the past.
"It's an important game because this is a period of the season that if we can keep our momentum going, we have got home games against Everton and Southampton in the next few weeks. These are really big opportunities for us."