A Taqele Naiyaravoro hat-trick inspired Warriors to a 43-6 win when the sides met at Scotstoun last weekend.
Hooker Brown - returning to the side after injury - expects Scarlets to provide a tougher test in the reverse fixture on Saturday.
"They'll be hurting after last week. It will be a tough game," Brown said.
Scarlets have been in impressive form in the Pro12 this season, winning eight of their nine matches to go top of the table.
However, they have lost all three of their Champions Cup matches so far, although Brown insists they will still be going all out to wreck Glasgow's European ambitions.
"The Scarlets will be a lot stronger this week I would have thought with a few players coming back in - and they're at home," he said.
"They'll be hurting after last week as well. No one enjoys getting beaten by 40 points.
"We've already lost to them once this year. We've had a lot of tough games down there. Two years ago, they gave us a bit of doing there at the end of the season.
"They might not necessarily have anything to play for in the competition, but that's a very dangerous thing as you never know what they're going to do against you."
After a troublesome foot problem that required surgery, Brown is back to fitness and relishing a return to action.
"It's nice to be back," he said. "The last eight weeks have been a bit frustrating.
"I've been waiting in the wings for the past week or two, so it's really good to be back this week.
"It's something I've had for a while. We've managed it here for maybe a year. It was just getting more and more difficult to manage for the last sort of six months.
"It was something that was maybe exacerbated at the World Cup just with so much in such a short period of time.
"It was something that had to get done at one point and it was just getting a bit too much to handle it.
"It was frustrating for me not being able to come back and play straight away.
"It's nice to be back involved training and playing this week."
Fraser Brown expects a backlash from Scarlets when Glasgow Warriors face the Welsh side a week on from their crushing Champions Cup victory.