The FA Cup-winning boss, 51, was caught by a speed camera as he drove his BMW along the Old Kent Road in Bermondsey, south London, last July.
Court records revealed Glasner already had previous driving offences on his record, leaving him in line for an automatic ban.
The Austrian wrote to Willesden Magistrates' Court in northwest London to plead guilty to speeding at 29mph on a stretch of the road which has a 20mph limit.
He also submitted a handwritten note promising not to break the law again, as he decided against trying to convince magistrates to spare him a disqualification.
"I fully accept responsibility for my actions and understand the seriousness of this matter," he said.
"I have taken steps to ensure it will not happen again.
"Due to the nature of my role, I will ensure I take the steps to address the issue."
A magistrate, sitting in private, imposed a six-month disqualification on Glasner on Tuesday of last week.
He must also pay a £660 fine, together with £130 costs and a £264 victim surcharge.
In May, Glasner guided Crystal Palace to FA Cup glory in his first full season in charge as the south London side lifted the first major trophy in their history.
Palace, however, were dramatically knocked out of this season's FA Cup in the third round by non-league Macclesfield in January.
Glasner announced the following week that he would leave the club when his contract expires at the end of the season.
This appeared to be a protest at a transfer policy that saw several high-profile players leave Palace, with those that remained at Selhurst Park "abandoned completely" by the Eagles' hierarchy, according to Glasner.
Palace are due to face struggling London rivals Tottenham later on Thursday, in a key match in the Premier League relegation battle, with Spurs just a point above the bottom three and the Eagles not yet out of danger themselves.
Glasner pleaded guilty in writing on January 27th and accepted that a ban would be imposed without an open court hearing in a second letter to the court on February 16th.
Details of the case have only now been revealed after Britain's Press Association news agency was given access to court documents earlier this week.