The Ibrox CEO announced in his business review last month that the League One champions' followers would no longer be able to pay for their season books using credit or debit cards.
That came after the firm processing the payments, First Data, demanded security over the stadium - a request Rangers rejected.
Wallace had claimed the firm's demand had been sparked by uncertainty over season-ticket sales following threats by fans to withhold their fees.
But in a question and answer session hosted on the club's official Twitter page, he insisted that was not a dig at the Light Blues faithful.
Wallace posted: "Just to be clear, fans were not blamed for the withdrawal of the credit card facility.
"The review said that negative comment in the media was a factor in the Club's credit card provider seeking security over Ibrox."
Reports this week suggest that as few as 2,000 of the club's 35,000 season ticket holders have renewed for next season.
Wallace admitted sales were "slow" but added: "[That's] understandable given the assurance fans have sought about the stability of the Club.
"Sales are gathering momentum now, as you would expect with the May 16 deadline approaching."
Wallace has also faced criticism from fans over a reported 100 per cent bonus he is entitled to, but the former Manchester City chief operating executive hinted he may not take the full amount.
"Any bonus that I may be awarded would be discretionary, based on a mix of company and personal performance," he said.
"This would be determined by the remuneration committee and any bonus for this year would only reflect the time I've been here."
After announcing his business review document - which outlined a cash burn of £70million over the last two years - Wallace admitted there would be a "small number" of redundancies amongst Ibrox workers.
But now he has suggested some of those affected may be given a reprieve.
He posted: "We are restructuring areas to better position us for future growth. As part of this, a small number of roles may be affected.
"We are working with everyone potentially impacted to identify if there are any potential alternatives for them."
Plans to honour the late Sandy Jardine were raised by supporters during the online Q&A and Wallace confirmed the club were hoping to unveil a lasting tribute to the European Cup Winners' Cup-winning defender.
"We sat down with Sandy and spoke with him at length about how we would like to mark his contribution to Rangers," replied Wallace.
"Discussions will continue with [his wife] Shona and the family to finalise the best way of recognising his service to the club."