Dallas left the SFA last Friday following an investigation into an e-mail which was sent around the time of the Pope's visit to Scotland.
Speaking about the controversy for the first time, Mr Salmond told MSPs yesterday: "The SFA, as a responsible organisation in Scotland, has rules and regulations covering these matters.
"I believe, incidentally, that following due process they have come to the right decision."
But the First Minister backed more protection for referees and voiced "sympathy" for official Dougie McDonald who quit last week after being caught up in a controversial penalty incident during a Premier League match between Dundee United and Celtic.
The First Minister told MSPs that the visit of Pope Benedict and a recent event commemorating the 450th anniversary of the reformation showed attitudes towards sectarianism in Scotland are changing.
"These two events and their reception from the overwhelming, vast majority of people in Scotland indicate that perhaps Scotland is beginning to win the battle against sectarianism and people of goodwill are uniting to win that battle," he added.
Peter Kearney, of the Catholic Media Office, called on the SFA to sack Dallas during the e-mail row. In the wake of his subsequent departure Mr Kearney blasted "anti-Catholic hostility" in Scotland.
Mr Dallas, himself a former referee, had been the SFA's head of referee development since June 2009.
He had been under increasing scrutiny over the past few weeks following his own handling of the aftermath of Mr McDonald's decision to rescind a penalty he had initially awarded to Celtic in a match against Dundee United.
It later emerged that the referee had exaggerated the role of his assistant Steven Craven when he explained the reasons for changing the decision to Celtic manager Neil Lennon. Mr Craven, himself, later quit.
Celtic chairman John Reid had publicly called for Mr McDonald to be sacked.The row over criticism faced by referees prompted officials to strike last weekend, with foreign officials flown in to take charge of SPL games.
But Mr Reid, a former Labour cabinet minister, came under fire from Tory MSP Ted Brocklebank during First Minister's Questions in parliament yesterday.
"It does little to douse the flames of sectarianism in football when chairmen of prominent Scottish football clubs go on television to demand the sacking of referees," Mr Brocklebank said.
A spokesman for Mr Salmond said he had "more sympathy" for the situation faced by Mr McDonald.
He said the First Minister was also supportive of plans to look at the introduction of a code to help assist referees in decision-making.
"Mistakes can be made, particulary given the highly charged nature of some matches," the spokesman added.
"It would be to the general benefit to the game if there was a degree of protection of referees in terms of the sort of measures in a code the SFA have said they are looking to bring forward."