Peter Hill-Wood has conceded that Arsenal cannot spend as much on players as the likes of Premier League rivals Manchester City and Chelsea.
The Gunners have failed to win a trophy for seven years and some fans have been frustrated with their activity in the transfer market during that period.
Hill-Wood says the club will continue to manage their finances carefully but is confident Arsene Wenger's team can mount a serious title challenge this term, while he found criticism of the manager last term 'disgusting'.
"Arsene has money to spend but there's a limit. We can't spend £50million on one player," Hill-Wood told the Evening Standard.
"At a certain level, we can't compete. I don't think [majority shareholder] Stan Kroenke is going to put the sort of dollars in that [Roman] Abramovich or Sheikh Mansour are putting into Chelsea or Manchester City. That's not the way he thinks clubs should be run.
"Luckily, Arsene understands that. He got an economics degree from Strasbourg University so he's certainly no fool. He knows how a club should be run. That annoys a lot of people but clubs have to be sustainable. We're not going to go bankrupt in the way one or two other well-known clubs have.
"The Glasgow Rangers example is something we've all got to guard against. They spent far more money than they could afford. We're ambitious enough but we're not going to end in the same plight as Rangers. That is a fact of life. So my advice is, don't get miserable about it."
Last season saw Wenger come under more pressure than ever since he took charge 16 years ago, with some fans even heard to chant: "You don't know what you're doing".
Hill-Wood said: "What those fans shouted did not influence me one little bit. I was disgusted to hear them because Arsene's been absolutely outstanding. He is still outstanding."
This summer saw captain Robin van Persie become the latest big name to quit the club because he did not believe their ambitions matched his own.
Hill-Wood said: "We have a pretty good chance of challenging for the Premiership. I don't see why we cannot win it this year."