Smith's departure was confirmed in a short statement on their official website and brought to an end his long association with the Dark Blues.
Asked how tough a decision it was to part company with Smith, Gardiner told Sky Sports News: "It was extremely difficult. It would be extremely difficult for anyone who knows anything about Dundee."
The 39-year-old captained the club and made 400 appearances as a player before returning to Dens Park as first team manager.
He also guided the club through their 2010-11 campaign - dubbed the 'Dee-Fiant' season - after Dundee retained their place in the Irn-Bru First Division despite a 25-point deduction for a second descent into administration.
However, results this season have left the club rooted to the bottom of the Clydesdale Bank Premier League, 15 points behind nearest rivals St Mirren.
Gardiner added: "The word legend is too often bandied about but he has been here for 17 years, through two administrations, coached the club, played for the club, captained the club, led it out at Hampden.
"He brought 'Dee-Fiance' after a 25-point deduction. Outrageous and amazing things. However football is a very cruel game."
The club statement read: "Dundee FC today announced that they have parted company with manager Barry Smith with immediate effect. Until matters regarding this have been formally concluded, no further statement will be made."
Dundee look set for a quick return to the First Division, following their hasty promotion to the SPL. They were late additions to the top flight in the summer, after replacing Rangers, and have struggled to compete throughout the campaign.
- Sports & Recreation