The Ayrshire band announced plans to play three nights at the Glasgow Barrowland earlier this week.
The concerts on December 5, 6 and 7 will give fans the chance to choose the band's set list, with each night focused around a different pair of albums from their back catalogue.
But music-lovers took to social networking sites yesterday to express their frustration after the tickets were sold within one minute.
The band had implemented additional measures including putting names on tickets and offering a larger percentage of tickets to members of their fan club in a bid to reduce the chance of touts getting the tickets. They are now asking any fans who see tickets for the shows being sold online to contact them.
In a statement, the band said: "Due to the unique fan-centric nature of these shows, we have done everything in our power, while planning these events, to try and manage this in an appropriate way, and to not treat these like our other shows.
"The Barrowland holds a special place in the band's heart and fits perfectly with the unique nature of the shows; sadly, however, it can't hold everyone who we know would like to go to these shows."