Brown insists Celtic's players are well aware of what is at stake against Shakhter Karagandy in the first leg of their Champions League play-off tie in the Astana Arena on Tuesday night.
Entry into the lucrative group stages of the competition for the second successive season could inject around £20million into the Parkhead coffers.
The Scotland midfielder believes his team-mates are focused on the job in hand and in even better shape to take that next step than they were a year ago.
"The players understand how huge this is, how big Celtic are and why we should be in the Champions League," he said.
"The two ties are huge, the biggest of the season and we are only three or four weeks in.
"We were back really early, it was a hard pre-season but we are starting to see the benefits now.
"I feel we are fitter and sharper than this time last season.
"Not having long off during the close season has helped get up to match speed quicker.
"But it is going to be very hard. We have seen videos of our opponents. A draw is a good result for us going back to Celtic Park."
Celtic will be asked again to play on an artificial surface after overcoming plastic pitches in earlier qualifiers against Cliftonville and Elfsborg.
Brown, though, is taking it in his stride, adding: "I don't think it is ideal for a qualification for the Champions League but we played on plastic in the last round in Elfsborg so we know what to expect."