"We are not contemplating them being nine points in front of us," said the England defender. "If it happens then it would be grit-your-teeth time for us.
"But we are not thinking about that. We just have to get our heads down and start winning.
"We know how strong Chelsea are at home. They have a great record there but it is imperative we get something out of the game."
On the face of it, a goalless draw against Villarreal at Old Trafford on Wednesday just saw United begin the defence of their Champions League trophy in the same manner as they started the season as a whole.
However, from his spot on the substitutes' bench, Brown felt there was enough evidence of improvement to fuel confidence in the Red Devils camp.
Sir Alex Ferguson does have defensive problems, caused by the absence of Nemanja Vidic.
"When you look at the striking talent on paper it is unbelievable," said Brown. "Once they start firing and we get a decent win under our belts, that strikeforce will be one of the best in Europe.
"No-one will relish playing against them. In the short time he has been here, Berbatov has shown everybody what he can provide for the team.
"As long as they can defend as well, it will be absolutely beautiful."