The Whites are currently sitting pretty at the top of League One, eight points clear with a game in hand, and Crowe believes winning at the Theatre of Dreams will see them continue their rich vein of form.
"To go to a place like that and win gives you an incredible feeling," he said in the Daily Star.
"If you have a good cup run, it breeds confidence and that can turn into a good league run as well."
The 31-year-old former Arsenal trainee moved to Leeds during the summer and only played on Sunday because regular right-back Leigh Bromby was suspended.
He cleared a Wayne Rooney effort off the line shortly after Beckford had put Leeds in front, and he admitted winning was a fantastic feeling.
"We always knew it was going to be tough, but we also knew we could give them a game," he added.
"But what a fantastic feeling. I didn't know what to say at the end. We gave United a good game and were delighted to win.
"We stayed strong as a unit and managed to keep a clean sheet.
"It was brilliant. You want to play in those games week in, week out. The dressing room was a fantastic place afterwards."
Leeds return to league duty on Saturday when struggling Wycombe make the journey to Elland Road.
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