Arsenal earned £26million from Europe last season but have endured a poor start to this campaign and are 15th in the Premier League table.
They are rare in being a top-flight club which makes a profit, and Gazidis told the Leaders in Football conference Champions League football was important, but not essential to Arsenal as a business.
He said: "We would rather qualify for it but we have a really sustainable model that can cope without it. Not just cope, but we can do well and compete.
"It would be very foolish to build a business model that relied on being in the Champions League for perpetuity and I don't think any clubs do that and, if they do, then they probably aren't being run as responsibly as they should be.
"Every club has the temptation to think that money is the answer to issues and 'if we only spend just a little bit more, it would push us over the top of a curve', and that is what drives the cycle of spending that you see in the game and that is not by any means always what is successful, actually.
"It is tempting to think that it is. It relieves pressure for a while but actually builds long-term pressure in other ways. We will continue to act with discipline to make sure we have got a good short-term and long-term future."
Gazidis also said Arsenal would be able to compete with the likes of Chelsea and the Manchester clubs in terms of player wages.
He added: "We don't have a salary ceiling. I don't know where that story comes from. We have a very sophisticated business model that looks at what we need to do to compete today and what we need to do to compete next year and five years from now.
"I'm comfortable we will be able to be competitive in whatever environment is created.
"We are not looking for credit for being a self-sustaining club. I do think it is the right model for us.
"It gives us stability and the ability to look forward with confidence without worrying too much about the ups and downs, the competitive cycle or the economic cycle."
Gazidis refused to be drawn on whether talks had taken place with captain Robin van Persie on a new deal - his current contract expires in 2013.
"I'm not going to comment on Robin," he said.