Wallace's comments came after the fans' group that arranged the meeting with major shareholder Laxey Partners this week issued a warning.
The London branch of the Rangers Supporters' Association has revealed they will consider not renewing season tickets if the current board survive the AGM next week.
Their actions will not adversely affect the finances of the SPFL League One leaders greatly due to the size of the organisation.
But the announcement comes the week after the three main Rangers supporters' groups, the Assembly, the Association and the Trust, threatened to "disengage" with the club.
And it gives a clear indication of the strength of feeling that exists among many of the Light Blues faithful about how their club is currently being run.
A London RFCSA statement read: "We are concerned that he (Laxey director Colin Kingsnorth) would not consider using his vote at the AGM to restructure the board.
"The overwhelming majority of Rangers supporters want change in the boardroom to restore our faith in the men who have stewardship over our club."
Wallace, meanwhile, has conceded Rangers have not engaged with their customers enough in his first interview since being appointed club chief executive.
He said: "Fans are the lifeblood, absolute lifeblood. We have a very significant fan base locally as well as globally. They have a loud voice and it's right that the club should listen to that voice.
"I think it's something in the past that we perhaps haven't done as well as we need to. And certainly it's part of my
philosophy is to engage with a wider fan base to understand the issues that matter to them so that we as a club can understand."
Wallace, the former Manchester City chief operating officer, stressed that making the team successful on the park is his top priority.
He said: "I think the key areas for us are to have the club performing well on the field because it is all about the football.
"That then allows us at a commercial level to be able to grow the business. And we absolutely need to be able to grow that corportate level, the right level of long term partnerships that then allow us to fund the ongoing developments in the club."