Jermaine Beckford stunned the home crowd on 19 minutes as he slotted the ball past United keeper Tomasz Kuszczak, and Leeds hung on for a famous win.
Bates, who took control of the club in 2005, thinks the upset demonstrated how far the side have come under manager Simon Grayson and hopes the result will accelerate the club's progress.
"It makes a change for Leeds to be in the headlines for what happens on the pitch," he said in the Daily Mail. "Of course Sunday was the stand-out day since I came to Leeds, partly because it was a good shop window for demonstrating how far we have come.
"Days like Sunday lead us to believe we might accelerate our plans for filling the ground again and getting back to the level where we think Leeds should be - among the elite in the country.
"As far as the side is concerned, we have come very close to parity against Liverpool (when Leeds lost 1-0 in the Carling Cup) and we felt we deserved to win at Old Trafford despite the added 'Fergie time'."
Bates took control of Leeds when they were embroiled in financial problems and during his tenure the club have never been far away from incident.
The 78-year-old has seen four managers come and go at Elland Road and during the 2007/08 season they were docked 15 points for entering administration.
However, the former Chelsea chairman admits he has a long-term vision for the club and that he is taking one step at a time.
"I don't think it is unrealistic to put a five-year plan forward as a target date, hopefully sooner," he added.
"There is no quick fix. This has been a tough experience and we have stepped back from the brink. People have worked with pride and we're on course for promotion.
"What is vital is that we are not living beyond our means, not starting with the roof when the foundations are made of sand.
"We are in a small profit-making position but it is essential we use our assets wisely."
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