The London club, who sit 15th in the league having endured their worst start to a season in 58 years, are widely regarded as one of the country's best run clubs and are one of just a few to make a profit.
They have enjoyed more than a decade of Champions League qualification and while it still remains a priority, Gazidis said it is not a necessity, unlike for other clubs facing huge wage bills and rising debt.
"We would rather qualify for it but [if we didn't qualify] we have got a really stable model that could not just cope but do well and compete," Gazidis told reporters at a Leaders in Football conference in London.
"It would be very foolish to build a business model that relied on being in the Champions League for perpetuity. 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."
European football's governing body UEFA introduced new Financial Fair Play (FFP) rules this season designed to prevent clubs spending more than they earn and Champions League revenues are seen as critical in order for top clubs to compete financially.
Last month Arsenal reported an operating profit of £45.8 million in the year to end May, down from £56.8million the year before as increased wage costs offset a rise in commercial revenue.
