However, he insisted the Gunners could still challenge for the title and that manager Arsene Wenger was not under pressure from the board to end a trophy drought spanning seven years.
Hill-Wood added he was "disgusted" by those fams who verbally abused French manager Wenger, in charge at the London club since 1996, last season.
"Arsene has money to spend but there's a limit," Hill-Wood told Tuesday's London Evening Standard. "We can't spend ?50 million on one player.
"At a certain level, we can't compete. I don't think (Arsenal 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," Hill-Wood added of the American sports entrepreneur
"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."
Hill-Wood cited the case of Scottish giants Rangers, now playing in their country's fourth-tier after entering administration, as "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 pre-season saw Arsenal captain Robin van Persie become the latest big name to quit the club because of their 'lack of ambition' but 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."
Source: AFP
Source: AFP