Gardner Speirs' side saw off Irn-Bru Third Division rivals Elgin City at Hampden on Saturday, with a strike from David Murray and Craig Smith's brace enough to clinch a 3-1 win.
The Spiders will travel to Fir Park in the fourth round in January, and Brough is looking forward to going head-to-head with the SPL high-flyers.
He said: "The guys were saying before the game what an incentive it was to go out and beat Elgin, not just for ourselves, but for the club as well, because they will benefit from it.
"It was a good performance from us on Saturday and we deserved to win the game.
"It is a fantastic tie for us to get at this stage and one I am sure we will enjoy.
"We have beaten Aberdeen not that long ago, and smaller teams have had a few decent results in cup competitions over the years.
"If we play well, then you never know what can happen. Of course, it is going to be a hard game for us and Motherwell will be huge favourites to win the tie through there.
"But we will go into it with nothing to lose, so we will just enjoy the game and see what happens."