They spoke out as Gaillard made a U-turn after branding Liverpool fans as "the worst in Europe".
Gaillard's comments came ahead of a report compiled for Uefa by under-cover police which was being revealed today.
The organisation said it would be handing the study to UK sports minister Richard Caborn during a meeting in Brussels.
But Gaillard, Uefa's director of communications, who said the report listed 25 incidents involving Liverpool fans since 2003, admitted it did not consider the severity of incidents.
He said: "There have been over 25 incidents involving Liverpool supporters since 2003, some of them small, some more worrisome."
Earlier this season, Dutch club Feyenoord were kicked out of the Uefa Cup for repeated crowd trouble.
Gaillard today said: "We cannot compare apples and oranges. The problems with Liverpool have not been big enough to earn the club any sanctions from Uefa.
"This is not about saying that Liverpool are the worst club."
Walton MP Peter Kilfoyle said: "Gaillard knew exactly what he was saying. The bottom line is that the organisation was a shambles and it's by the grace of God it didn't turn out much worse. I don't think he should resign - I think he should be sacked. For him to resign would be a way out with honour."
Riverside MP Louise Ellman said: "He should substantiate his statement or resign.
"It is totally unacceptable for him to make slurs of this serious nature when the fault clearly lies with the authorities."
Wavertree MP Jane Kennedy said: "Uefa have tried to deflect the criticism from their handling of this from the start."
Knowsley MP George Howarth said: "Uefa's arrangements were woeful."
Reds chief executive Rick Parry said: "What is most surprising about the latest comments from Mr Gaillard is that on the eve of the final, he quite rightly commented that Liverpool supporters 'have a tradition of good behaviour'."