The Welsh attacker, who has been subject of an enquiry from the Red Devils, admitted that the veteran's decision to call it a day came as a shock at the Spurs training ground
Sir Alex announced his decision to step down on Wednesday after 26 and a half years at the Old Trafford helm.
And Bale, who would cost United £70 million if they were to make a summer move, admitted the decision came out of the blue.
|7/4||Tottenham are 7/4 with Bet365 to finish in the top four
"It was a massive shock to me and a few of the lads at the training ground, it will be very strange to go to Old Trafford without Alex Ferguson there."
David Moyes has been appointed as Sir Alex's successor on a six-year deal, and while Bale admits he is likely to carry on the 71-year-old's good work, there is scope for a rough bedding-in period.
"I'm sure now they've gone with the new appointment he will be there overlooking everything and making sure everything's smooth," he added.
"Once the new manager comes in you'll see how they hit the ground running. If there are any problems there I think that might give other teams confidence. I thnk it's all about waiting until next season and seeing how things go."
Sir Alex will bid farewell to United fans after the game against Swansea at Old Trafford on Sunday, while Tottenham keep up their quest for Champions League football away to Stoke.