The defender said: "I think the first goal will shape the game and hopefully it goes our way. We'll be approaching the game as we would any other, no matter that we're 2-0 up. We can't afford to sit back because if they get a goal they're well and truly back in it.
"We'll be looking to score first because that gives us a great chance. At the same time we can't be gung-ho but if we get some chances we'll focus on putting them away."
Brown also warned that Roma will be out for revenge after they humiliating 7-1 defeat to United at the same stage last season.
He added: "It'll be a difficult game and they'll be coming here thinking they've still got a lot to play for. The 7-1 game will be in the minds of those Roma players who played because it's not a nice thing to be involved in.
"And I'm sure they'll be going for revenge, so everyone will have to be on their toes."