The Hoops skipper believes it is time for UEFA to rank individual clubs on past performances in the competition rather than judge teams by the status of their national leagues.
UEFA’s system of coefficients places the Scottish Premiership 23rd out of Europe’s 54 top-flight leagues.
This means Celtic must start their European campaign in the middle of July, despite battling their way into the group stages of the Champions League twice during the last three seasons, and in seven of the past 12.
Icelandic minnows Stjarnan are Celtic’s first opponents – they face them in Glasgow on July 15 – and Brown is also frustrated at having to start the season earlier than normal, and often against teams whose national leagues play through the northern hemisphere summer.
The 30-year-old said: “It’s always hard having just the two weeks off when you are the champions. People don’t appreciate us as much as they should.
“When we play in the Champions League, whether it’s home or away, we always give it a right good go. We’ve done well in the past and hopefully we will do the same this season.
“It might happen in the future that your coefficient is worked out on what each club does rather than all the teams from your league.
“But the way it is now we need to deal with the three qualifiers that are coming towards us. We have to try and get through them and do as well as we possibly can.
“The first Champions League qualifiers are always hard because they (opponents) are six or seven weeks ahead of us in their league, so we are always playing catch-up. But hopefully our quality shines through.”
However, Brown accepts that the life of the modern professional means they almost have to accept wall-to-wall football: “I had a two-week holiday and I also had a week off before meeting up with Scotland so I’ve definitely had enough time to recharge the batteries.
“I think that’s just modern Scottish football. Due to the number of qualifiers for the Champions League that’s what it’s going to be like.
“I don’t worry about anything like burnout. It’s just something you put in people’s heads but it’s an excuse to be perfectly honest.
“The lads work hard and want to play week-in, week-out. We played 55 games last season with the same holiday break we’re getting this time. I’m sure we can do just as well this season.”