Phaedra Al Majid says she invented the claims that Qatar 2022's World Cup bid had bribed FIFA members in return for votes as revenge for losing her job.
The claims she made to the Sunday Times were made public by Parliament's culture, media and sport committee in May.
Robertson backed the committee's decision to make those allegations public and said FIFA should not be let off the hook - especially with other corruption cases still to be dealt with by the organisation.
Robertson told Press Association Sport: "I do not think this dilutes the case for substantial reform of FIFA one bit. There are still many other issues that it faces.
"I have just come back from the International Olympic Committee session in Durban last week where they had the vote for the 2018 Winter Olympics and there was absolutely nothing that questioned the fundamental integrity of that process.
"That is how it needs to be for FIFA - they have got to get themselves into that position too. They are not anywhere near there at the moment."
FIFA's ethics committee meets next week to hear the case of Mohamed Bin Hammam, the FIFA member suspended on charges of bribing members of the Caribbean Football Union.
FIFA dropped the investigation against Jack Warner, the FIFA vice-president who was also suspended, after he resigned from football-related activities.
Robertson said that the select committee had been right to make the whistleblower's claims public.
He said: "They would have been heavily criticised if they had not put that information into the public domain.
"I am entirely supportive of their decision to do so. The can only act on the information that is put in front of them."