Celtic travel to Sweden on Tuesday defending a 1-0 lead in the third qualifying round of the Champions League ahead of Wednesday's game.
Kris Commons' late header put them in the driving seat and Brown believes they can take encouragement from last season's run to the last 16 of the Champions League.
Brown 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."
One of their games on artificial turf was in the Luzhniki Stadium last season when Celtic finally broke their unwanted record of never having won an away match in the Champions League proper with a 3-2 win over Spartak Moscow.
"It was huge," Brown said. "I think it was hanging over everyone's head at Celtic, the players and supporters as well. We seemed to think we were never going to get there.
"This is a club who can go away from home now and get a good result.
"We won a few qualifiers away from home as well."
Celtic came within seconds of getting a point in the Nou Camp before beating Barcelona at home and Brown feels the memory of their run to the last 16 can drive them on.
"It gives us confidence, especially away from home," he said.
"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 produced a stuffy and physical performance at Parkhead but Celtic could benefit from their need to come out and chase the deficit.
"Elfsborg came out with a game plan at Celtic Park and they stuck to it," the Scotland midfielder said.
"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."