Peter Hill-Wood reiterated the club's desire to live within their means, saying majority shareholder Stan Kroenke would never pump in money like the owners of Chelsea and Manchester City.
The Arsenal chairman also revealed that contract talks with Theo Walcott were at a standstill while reposing his faith in Arsene Wenger and his ability to bring back the Gunners some major silverware.
"At a certain level, we can't compete," Hill-Wood told the Evening Standard. "I don't think 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."
However, Arsenal have gone without a single trophy for over seven years, while the likes of Chelsea and Manchester City are winning silverware thanks to their sizeable investments. Arsenal fans were further incensed this year, when they sold their best player -Robin Van Persie - to title rivals Manchester United, while Walcott is yet to sign a new contract with less than a year remaining in his current deal. Hill-Wood, however, said he is not too concerned about the lack of trophies, words that are sure to disappoint Arsenal fans even more.
"It is not a worry to the board that we haven't won a trophy since 2005," he said. "It would be lovely to win but it's not that easy.
"Liverpool haven't won the title for 20-odd years. We're very ambitious and want to win but, if you don't have billions of petro-dollars to throw around, you're going to have to do it some other way.
"That's what we're trying to do -- with skilful selection of players. As for Walcott, he did not accept our offer so nothing is happening."
Some fans and pundits alike have pointed to the firing of Wenger's close friend David Dein in 2007 as a major reason in Arsenal failing to compete consistently at the highest level. "I don't think David Dein's departure has impacted on Arsene at all," he said. "Arsene has a very good relationship with (chief executive) Ivan (Gazidis) and it's very businesslike. He and Arsene get on very well."
Hill-Wood also expects Wenger to see out his career at Arsenal. "You occasionally hear rumors of him going somewhere," he said. "I do not think that is likely to happen.
"He's very happy where he is. He has a very good job in that we don't interfere with him. We agree with most of the things he says and he agrees with most of the things we say. I have seen some really successful Arsenal managers but Arsene has revolutionised the club.
"I would say he has been a bigger influence than Alex Ferguson on Manchester United in the way he has changed the traditions of the club and the outlook of the Premiership."
