The Ibrox chief made the comments during a Q&A with fans on Twitter, where he faced a barrage of tweets from angry supporters.
While empathising with fans, he also defended his right to a bonus and urged fans to get behind the club in the face of “slow” season ticket renewals.
He wrote: “I can understand the fans having msitrust after what has happened to the club in recent years.
The board is working hard to earn the trust and respect of our fans.”
Wallace, who spent 90 minutes answering 15 questions from a list of hundreds, also said he was “proud” to be in charge of Rangers.
“I absolutely care about the club personally and professionally. We have a big job to do here and I am proud to be Rangers’ CEO.”
Answering a question about justifying a 100 per cent bonus on top of a £315,000 salary, Wallace said: “Any bonus I may be awarded would be discretionary, based on a mix of company and personal performance. This would be determined by the remuneration committee and any bonus for this year would only reflect the time I have been here.”
Wallace said season ticket renewals were gathering momentum, despite two Rangers fans’ groups announcing a boycott of season tickets. But the chief executive admitted the sluggish take-up on tickets was understandable given the uncertainties surrounding the club’s stability.