The Gunners quest for a first trophy since 2005 suffered another blow on Tuesday night when they were beaten on penalties by npower League Two side Bradford at Valley Parade.
The Arsenal Supporters Trust have long supported the Gunners' prudent financial approach, but believe the lack of spending has now gone too far - and that the defeat by Bradford was a symbolic moment with the team having decreased in quality year after year since 2009.
However, in a wide-ranging interview with the January edition of Four Four Two magazine, Gunners chief executive Gazidis insisted the club's self-sustaining business model will pay off in the long term.
"If you do any analysis of performance against spending over the past 15 years, Arsenal is the one club which has outperformed its spend every single year over that period," Gazidis told the magazine.
"That does not happen by accident; it happens because we have an outstanding manager who is an outstanding judge of talent and very experienced in how to manage a team.
"There are some real fundamentals at this club which I think our fans believe in - we stand on our own two feet and take pride in our achievements.
"We are not reliant on anyone else for success. That is the model our fans believe in, and for good reason."
Last month, Arsenal announced an extension to the sponsorship deal of Emirates Airline, which will be worth around £30million a year.
Gazidis, however, insists simply throwing all of that cash at the team is not the answer for a quick fix.
"I am not sure what the alternative strategy is, it has not really ever been spelt out," he said.
"I assume the alternative strategy is to spend more than the nation state of Abu Dhabi, more than anyone else, and I am not even sure I would describe that as a strategy, but it is the only other thought that comes to mind."
Gazidis met members of the Arsenal Supporters' Trust on Wednesday where he was pressed on the deepening crisis at the club.
"(Tuesday night) was simply not good enough and it made us all upset and angry," he said in quotes reported by several national newspapers.
"I would like to apologise to all of you (the supporters), especially the fans who travelled up there. It was unbelievable support as ever and you deserved better.
"That is something we will work hard to put right. We all work here and are desperate to deliver the success and trophies we all want. Look into the eyes of the staff here, look at the way they all talk. We will get this right."
The Trust wants changes at board level, for Wenger to release some of his duties to others, and for the manager to spend some of the many millions available to him.
Even if results do not pick up, Wenger's position should be safe at least until the end of the season but an increasing worry for club executives is that significant numbers of fans are not turning up to matches at the Emirates despite having bought tickets.
There is also growing frustration that players brought in since the departures of Cesc Fabregas, Samir Nasri and Robin van Persie have failed to deliver.
Even Arsenal's honorary vice-president Lady Nina Bracewell-Smith expressed that frustration on Wednesday, saying on Twitter - though deleting it soon afterwards, that: "Gervinho is a FLOP player".
There is also a fear that Theo Walcott may also leave the club - especially with Manchester United now linked with the England forward.