"Fraizer's only been around the place for three days and he's played two games," Brown told Hull's official club website. "He wants minutes on the pitch.
"He got that on Saturday but he didn't get any chances. Last night he had three or four decent chances, albeit a couple from long range and he took two of them."
Campbell's pace and eye for goal were a constant thorn in the Tykes' side on Monday, and Brown expects the youngster to hassle defences at the top level of football.
"He's bright, lively and confident," he said. "He has good movement and an eye for goal and that's why we've brought him to the football club.
"You would hope he's got what it takes to play at the top level. He's only 20 and the reason he is here is to get experience at Championship level and then go back as a United player.
"That is the nature of the deal and I understand that. We'll do right by the player while he's here. I'm sure the United connections watching last night know what they've got. He showed the bit of class that he has."