The Scottish Premiership champions take a fragile 1-0 lead to Sweden as they look to force their way into Europe's elite club competition again - but Brown is confident of conquering the Elfsborg playing surface.
The Scotland international said: "It's going to be hard, it's on astroturf. We have been training on astroturf for a few days trying to get our heads around it.
"We won't know what kind it is until we get there. But we are not worried. We have had a lot of games on it in the last few seasons and are getting quite used to it.
"There was talk about it in the past, about us struggling away from home and getting beat in every game, but now we seem to be winning away from home as well. That's what the gaffer has instilled in us.
"Elfsborg came to Parkhead with a plan and they stuck to it. They tried to defend and sneak a goal at the end hoping to get a draw so they could take us back to the astro-pitch. We did well on the night, though, and even though they were 16 games into their season we looked a lot fitter than them.
"We've not really had a long break so match fitness has caught up quite quickly. The lads look sharp in training as well as the games."