Nasdaq said in a filing with the Securities and Exchange Commission (SEC) late on Thursday that Greifeld's bonus for 2012 fell 62 percent to $1.35 million.
(Read More: Citi Claims with Nasdaq for Facebook IPO: Sources)
The mishandling of Facebook's IPO also cost Anna Ewing, Nasdaq's executive vice president of Global Technology Solutions, a $263,625 cut to her bonus for 2012.
"The committee and board explicitly considered the Facebook IPO in connection with their review and determination of these reduced payouts," the company said in a filing.
(Read More: Suckers! Tech Execs Selling Stock at Record Pace)
Facebook's eagerly anticipated listing on May 18, which raised $16 billion, was initially delayed by 30 minutes due to a technical glitch at Nasdaq.
The exchange then made the decision to get the stock trading by using a secondary system that ended up leading to delays in many clients' orders and confirmations, costing some investors big losses as the stock price dropped after an initial gain.
In March, U.S. regulators approved Nasdaq's $62 million compensation plan for firms that lost money in Facebook's market debut, far less than the $500 million in estimated losses.
(Read More: How Facebook Can Finally Cash In on Instagram)