Nasdaq OMX Group Chief Executive Officer Robert Greifeld says the exchange is embarrassed over the way it handled the Facebook initial public offering, which was marred by technical glitches.

"We have been embarrassed and certainly we apologize to the industry," Greifeld tells CNBC, adding the exchange isn't on the hook for any losses sustained by retail investors.

Technical glitches failed to properly execute buy and sell orders, delaying the May 18 IPO.

Editor's Note: How You Lost $85,000 During the Last Decade. See the Numbers.

The Nasdaq has proposed a compensation package worth $40 million for some financial institutions who lost money amid mishandled trades during the IPO.

"As an exchange, we have registered broker-dealers as our customers," Greifeld tells the network.

"The registered broker-dealers have the retail and institutional investors. So as we look to our accommodation policy, we’re not privy to what happened at the retail level. So we obviously can only focus on what we see, and that’s our transaction with our member customers."

Some say the compensation falls short, including Knight Capital in Jersey City, New Jersey, which estimates it lost up to $35 million in the IPO, according to Bloomberg.

Knight Capital is executes orders for individual investors sent to the firm from retail brokers.

"Clearly, we are disappointed that Nasdaq’s compensation fund does not come close to covering reported losses from broker-dealers like Knight who traded Facebook shares on behalf of average investors the day of the IPO, and who suffered losses as a result of Nasdaq’s failures in connection with this IPO," Knight says in a statement, Bloomberg adds.

"Their proposed solution to this problem is simply unacceptable. As previously stated, the company is evaluating all remedies available under law."

Technical glitches weren't the only dark cloud marring the IPO.

Investors have ditched the stock, initially priced at $38 a share, on sentiment the company was overvalued, as despite having 900 million users, monetizing that base may prove difficult.

Facebook is trading below $27 a share.

Editor's Note: How You Lost $85,000 During the Last Decade. See the Numbers.