Wednesday saw SFA chief executive Smith reveal a draft proposal for a radical overhaul of the under-fire procedures was set to be submitted to the organisation's board for approval.
Smith's statement came just hours after Scottish Premier League counterpart Neil Doncaster revealed he had written to the SFA to add his voice to the growing clamour for reform.
The main concern expressed by Doncaster, the Scottish Professional Footballers' Association and a number of clubs - including Celtic - was the ability of match referees to veto appeals for wrongful dismissal after viewing a video of any incident.
It is understood the new proposals would strip officials of these powers and establish a three-strong appeals panel, which would decide whether to reject or uphold a referee's original verdict.
Smith claimed in his statement he had been working on these changes for "some time" but Reid today suggested the SFA chief had bowed to pressure from himself and other parties, saying: "As a club, we welcome Gordon Smith's change of heart with regards to adapting the appeals process within Scottish football and hope we can now proceed to a fairer and more satisfactory system."
Celtic were highly critical of the SFA disciplinary process after captain Scott Brown was sent off by Dougie McDonald in February's Old Firm derby at Ibrox and the referee opted to stand by his decision.
Responding to possible changes to the appeals procedure, Hamilton manager Billy Reid said: "Whatever rules they make up, we have got to adhere to.
"A lot of people have commented on the whole thing but I don't really have too many views on it.
"There will be a committee which will sit down to decide what is happening and Hamilton Accies will go along with whatever the rules are."