Over 30,000 tickets have already been sold for the 60,000 capacity ground.
Speaking to BBC Scotland, Price said: "We've all seen Celtic on European nights and it's a brilliant stadium when it's full.
"I'd like to think now that we're in the final we can go a fair way in doing that and getting that sort of atmosphere. The stands are close to the pitch, right on top of the game."
Price scored the second of Glasgow's seven tries on a noisy night at Scotstoun.
Wariors have added a more ruthless edge to their play in recent weeks and the Ulstermen couldn't match the host's intensity.
Price believes the heavy defeat to Saracens in the Champions Cup quarter-final in March was a lesson on what is required to compete with the very best.
"It took us to get turned over by Saracens, that was the kick up the arse," said the Scotland international.
"It shouldn't have happened in a quarter-final of Europe but that's when it happened. It's a weird thing the mindset, getting everyone focused on the same thing and getting the mentality right.
"The boys up front have been outstanding in the last four of five games. It gives us quick ball and we've got the back division to give teams trouble when we get that quick ball.
"It all comes down to getting those hard yards up front and being brutal at rucks. We've got one more week and I'm sure the big boys will turn up again."
Friday marked Stuart Hogg's final appearance at Scotstoun before his summer departure for Exeter Chiefs, and Price shared a few words with his friend and team-mate at the full-time whistle.
"I said, 'We've done it mate, we've made it to the big one', Price revealed.
"We've not mentioned much about this being his last game at Scotstoun. For him there would be nothing better than to send him on his way by winning the title. We've given ourselves that chance.
"I just told him, 'We've got one more week bro, we're back in Monday'."