Eric Milligan, chairman of the capital's licensing board, said there was a perception that Glasgow's administration of liquor laws was still anti-alcohol, a reflection of the Temperance Movement.
The Labour councillor said thousands of Hibs and Hearts fans who came to Glasgow for the Scottish Cup final in May had problems accessing pubs.
Mr Milligan, Lord Provost from 1996 to 2003, urged the Games' hosts to learn from Edinburgh's experience in 1970, when the easing of the 10pm pub curfew set the blueprint for the relaxation of Scotland's licensing system several years later.
However, Malcolm Cunning, chairman of Glasgow's licensing board, argued historic reasons and health statistics lay behind the capital's reputation of having a more liberal approach, casting doubt on the scope for permanent change.
One former senior member of the Glasgow board described colleagues in his tenure as being "socially conservative, scared of the Calvinist/Catholic approach to alcohol" and suffering an "80-year-old hangover from the Temperance movement".
Pubs and clubs in Glasgow are expected to be given extra opening hours during the Games as happened during the city's Year of Culture in 1990.
As well as the 11 days of the core event, there will also be the Queen's Baton Rally, the equivalent of the Olympic torch, and cultural events.
While acknowledging that, in the past six months there had been a fresher approach by the Glasgow board to licensing, Mr Milligan said the perception was of the city being uptight.
He said: "There are areas of Glasgow where the legacy of the Temperance Movement is still clear and there are very, very few licensed premises. And we know there are areas where licensed premises in the city are still frowned upon.
"Before and after the cup final the supporters struggled to find anywhere for a drink and had to head home for either a celebratory or consolation pint.
"The Temperance Movement has a connection with the Co-operative Movement and has always had an appeal for many in the Labour Party.
"I don't want to get drawn into Glasgow stereotypes but Edinburgh is more bourgeois, something which has ups and downs.
"Social attitudes are different. But Glasgow has the oppor-tunity to put on its best possible welcome here to people who have never been in the city and would maybe never had heard of it if it weren't for 2014.
"It needs to send out the message that this is something very special and special decisions need to be taken to create the right mood."
Andy Muir, vice-chairman of the Glasgow board between 2009 and 2012, said he had "found the agenda setting and decisions made socially conservative".
He added: "The advice always erred on the side of caution.
"It was always unclear to me if that came from higher powers from within the council, an 80-year-old hangover from the Temperance movement or the powers that be were scared of the Calvinist/Catholic approach that comes with alcohol in Glasgow."
Mr Cunning said: "There's a more relaxed attitude in Edinburgh to licensing but I'd always put this down as coming from the festival. There was no licensing legacy from the Year of Culture and perhaps the attitude in Glasgow has been shaped by a variety of historic reasons and health statistics.
"We've got to look at how the board will go about things with a view to 2014. But is 11 days of sport really going to lead to any change?"