But Hill-Wood was confident the Gunners would mount a serious title challenge this season and insisted the board were not worried about Arsene Wenger's failure to win a trophy for seven years. The Arsenal chairman also said he was "disgusted" by those fans who abused manager Wenger last season as the club once again came up short.
Hill-Wood told the Evening Standard: "Arsene has money to spend but there's a limit. We can't spend £50 million on one player. 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. "
He added: "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."
- Arsene Wenger