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updated 1/3/2014 12:48:41 PM ET 2014-01-03T17:48:41

Despite warnings on Christmas Eve by an internet security group that a potential attack was looming, Snapchat chief executive Evan Spiegel said with a nervous laugh on the Today show this morning, "At the time, we thought we had done enough."

But then, on New Year's Day, the names and phone numbers of 4.6 million uesrs were leaked by anonymous hackers onto the website SnapchatDB.info, which has since been taken down.

While he didn't offer much in the way of an apology, Spiegel reasoned that tech startups teetering on the brink of innovation are particularly vulnerable to unforeseen abuses. "In a business that's moving so quickly," he explained, "if you spend your time looking backwards, you're just going to kill yourself."

Related: Happy New Year? Snapchat and Skype Get Hacked

Snapchat announced today a new version of its app that allows users to opt out of the Find Friends feature -- the cause of the breach. And looking ahead, Spiegel assured the app's users -- who send 350 million images a day, the company said -- that security would be top of mind.

"You have to work really, really, really, hard with law enforcement, with security experts, internal and external groups to make sure you're paying attention and addressing security concerns," Spiegel explained.

Snapchat also noted that no images or videos were compromised during the attack.

You can watch Spiegel's full interview with the Today show here:

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