The rules of the competition mean that Burton will be entitled to 45% of the gate receipts from Old Trafford, which has a 75,000 capacity, as well as a TV broadcast fee and a reward fee for making it through to the third round.
As a result, Clough says that the game has provided a "big boost" financially ahead of the January transfer window and will go on to account for 20% of the Championship side's budget for the season - the equivalent of a 25% rise.
"I thought it was absolutely incredible when [the draw] came out," Clough told talkSPORT. "We had an unbelievably tough tie at Cardiff in the previous round and to get drawn at Manchester United is still the one that everyone wants.
"It's a big boost for us and will give us about 20% of our total budget for this season, just from one game.
"We've got things to do with the ground, and things to do with the team in January and it just takes a bit of pressure off us financially.
"It's wonderful, but we look beyond that. It's great for the chairman but we just want our players to experience playing there."
The Brewers have had a mixed start to the new Championship season, taking eight points from the first eight fixtures of the campaign.