But he did not do enough to earn a contract with the Yorshire side, although the Millers' boss Mark Robins had words of praise for the player.
"What you see with Drewe is what you get. He wears his heart on his sleeve, I thought that he got hold of the ball and brought other players into play," he said.
"I just thought that it didn't happen for him, as with everybody in the first third of the game, because everything was very narrow and passes were running two or three yards apart.
"I won't be pursuing the situation with Drewe, but I thank him for his efforts while he's been with us."
There was better news for the former Plymouth and Brentford youngster Reid though, who is being offered a deal after impressing against United and in a previous game against Derby County.
Reid, 19, came through the youth team ranks at Plymouth Argyle and made 12 first-team appearances for the Pilgrims before joining Brentford in February.
"I've been impressed by what I've seen of him and I'll be looking to offer him something," added Robins.