Myles Weston scored twice and Sam Wood added a third, while Ian Harte's penalty was the only response Carlisle could muster.
"We thoroughly deserved to win the game," Scott said. "It was a dominant performance and we could have had seven or eight goals."
The Bees boss praised Weston after the former Notts County man's debut double.
"There's something I like about him and he could have had another goal because we created some very good chances," added Scott.
"This is a progression from last season. We knew we had plenty in the tank and looked very comfortable."