Alerts sent to users will now include one when data is restored to a new device, Mr Cook told the Wall Street Journal.
iCloud accounts may been broken into when hackers correctly guessed passwords or through phishing, he said.
But Apple's security had not been breached.
The company already alerts users by email when a new device tries to gain access to data and when someone tries to change a password.
Apple will start sending push notifications about activity on user accounts in about two weeks.
"When I step back from this terrible scenario that happened and say what more could we have done, I think about the awareness piece," he told the Wall Street Journal. "I think we have a responsibility to ratchet that up. That's not really an engineering thing."
Intimate pictures of a number of personalities were published online this week.
Actress Jennifer Lawrence confirmed a leaked topless photo of her was genuine.