"It's amazing that both Bats and Nasdaq unfortunately failed in an inglorious way," said William Karsh, the former chief operating officer at Direct Edge Holdings, an exchange operator that competes with Nasdaq.
"It proves that technology isn't infallible," he said.
The US Securities and Exchange Commission said it would review the trading.
Jonathan Thaw, a spokesman for California-based Facebook, declined to comment.
"This was not our finest hour," Greifeld said, after Nasdaq's board convened to discuss the offering.
Asked if his job was secure, he said, "I certainly hope so."
Nasdaq will use an "accommodation pool" to pay back investors who should have received executions in the opening auction, based on the decisions of a third-party reviewer, Greifeld said.
It may total US$13 million, he said.
Problems surfaced on May 18 at 11.11am New York time after Morgan Stanley, one of the underwriters that sold 421 million shares the night before, completed its role setting the price for the trade in Nasdaq's opening auction, Greifeld said.
Nasdaq's software for IPOs allows investors to cancel or update details of orders until the auction runs.
Trade requests received during the 5 milliseconds it took to operate the auction disturbed the process, leading to an imbalance of buys and sells and sending the program into a loop.
Nasdaq officials manually intervened to allow the auction to occur at 11.30am.
The IPO software "didn't work" even after thousands of hours of testing for "a hundred scenarios" aimed at anticipating problems, Greifeld said.
"We're not happy with our performance," he said.
Volume during the auction amounted to 75.7 million shares, or almost 1 per cent of trading during the entire day on all US exchanges, according to data compiled by Bloomberg.
"We saw on a real-time basis, obviously with the pressure of the world upon us, that this was happening," Greifeld said.
"We then manually intercepted this cross. That manual intervention said we had to ignore the cancels that came in between the raindrops as we were processing the trade."
Orders totalling 30 million shares were submitted into the opening auction between 11.11am and 11.30am, Greifeld said.
About half of them may involve "some level of dispute".
Greifeld said he didn't think the delay in starting trading affected the price of Facebook shares.
Adding to the day's confusion, Nasdaq reported an issue after trading began with confirming transactions from the opening auction with the brokerages that placed them.
The exchange said in a statement posted to its website at 11.59am New York time that it was having a problem delivering the messages.
An update at about 1.57pm said they had been sent.
- BLOOMBERG