Wallace took to social networking site Twitter for over an hour yesterday to answer questions from concerned Light Blues supporters.
The 52-year-old interacted with followers of the SPFL League One champions as part of the "Ready to Listen" initiative he launched earlier this season.
He responded to a wide-ranging series of queries - including those about season ticket sales, the scouting network, the withdrawal of credit and debit card facilities, his personal bonus and redundancies.
Some Gers supporters congratulated the chief executive for taking the time to engage with them.
Gary McDonald responded: "Well done to him. How many CEOs have done the same?"
However, many more were unhappy with his answers. Rangers fan Ally Mackay said: "He ignored what needed answered. It was a complete waste of time in my opinion."
Shirley Grant said: "He cherry-picked the questions he answered."
Wallace, who earns £315,000 per year in his role, appeared to dismiss widespread suggestions that he would receive a substantial 100% bonus this year.
He said: "Any bonus that I may be awarded would be discretionary based on a mix of company and personal performance. This would be determined by the remuneration committee. Any bonus for this year would only reflect the time I've been here."
The former Manchester City financial officer and chief executive has been criticised for not turning down a bonus at a time when staff are being replaced.
He stated: "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."
Wallace attempted to clarify reports that the club had claimed fans threatening to withhold season ticket money had been responsible for having their credit and debit card facilities withdrawn.
It has been alleged that First Data withdrew their services in January - before the prospect of fans not renewing their season tickets had been made public in February.
But Wallace stressed: "Just to be clear, fans were not blamed for the withdrawal of the credit card facility. The review said negative comment in the media was a factor in the club's credit card provider seeking security over Ibrox."
Elsewhere, he reiterated that season ticket sales had been "slow" - before revealing that they had been "gathering momentum" as the May 16 deadline drew nearer.
He said: "Season ticket renewals have been slow. It is understandable given the assurance fans have sought about the stability of the club. But sales are gathering momentum now as you would expect with the May 16 deadline approaching."
Wallace stressed that setting up an extensive scouting network - there is not currently one in place - was a priority for the club as they attempt to return to the top flight of Scottish football.
He said: "We're in the process of rebuilding our off-field football support. Key focus is a quality scouting and recruitment structure. In addition, we are putting focus behind long-term player development to identify future talent for Rangers.
"The manager is working on strengthening the squad for next season. Some changes have already been made, some are still to come.
"I absolutely care about the club both personally and professionally. We have a big job to do here and I am proud to be Rangers CEO."
Wallace also confirmed that talks had taken place about how to honour the late Ibrox legend Sandy Jardine for his outstanding service to the club.
He said: "We sat down with Sandy and spoke to him at length about how we would like to mark his contribution to Rangers. Discussions will continue with Shona (his wife) and the family to finalise the best way of recognising his service to the club."