The Hoops are looking to knock their opponents out of the qualifiers for the second year running after a 3-1 first-leg win at Parkhead last week.
Instead of simply sitting on their current advantage, Brown wants to make sure of progress with a victorious display in Trondheim on Wednesday.
"The football we played in the second half was outstanding," the Bhoys captain told Sky Sports News. "We managed to keep them back in their half and keep the shots on Craig's goal to a bare minimum.
"The way the lads played was exceptional but going over there is totally different circumstances. They know they have to come out and score two goals so here's hoping we can open them up a little bit.
"We have won there before so the aim for us is to go over there, score goals, create chances and play good football. We believe we can do that."
The winner of the tie faces AEK Athens in the third qualifying round.