"Well, Carl Icahn is one smart guy," he said. "But the reality is Apple is about building great products, great experiences, and if I were Tim Cook, I'd deal with him the way Steve Jobs would probably with him—not blink."
Sculley, who was Apple's chief executive from 1983 to 1993, said that Apple's cash could be put to better use.
"I would continue to invest in the business and grow the platforms they have," he said. "There's still a lot of growth ahead for Apple without having to use the—what I'd call the old recourse many companies follow when they don't have big ideas like Apple and just go in and buy their stock back or make bigger dividends.
"Apple doesn't need to do that. It still has a growth story ahead of it, and it's been way, way underestimated, I think, in the things it can do beyond the hardware, cool devices."
Sculley praised the new iPhone 5s' 64-bit A7 chip, calling it an "incredible processor."
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"It's 40 times more powerful than their original processor in the first iPhone, the first iPad. And they've only begun to tap the capabilities," he said.
The new iPhone's fingerprint-activated Touch ID, its e-commerce-enabled Passbook and Apple's industry-disrupting track record meant great potential, Sculley said.
"What if Apple went out and instead of buying their stock back the way Carl Icahn has proposed, what if they went out and bought eBay? And they'd use all of the capabilities that I just mentioned," he added. "They could game-change e-commerce almost overnight, and it would shift the balance of power to Apple in a way they don't have today."
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Sculley added that he wasn't expecting to see a repeat of the showmanship of late co-founder and CEO Steve Jobs.
"What I'm looking for is, really, how do you take advantage of this incredible ecosystem Apple has and technologies, and start to connect the dots and maybe do game changes where you can disrupt an entire industry, not just have another cool product," he said.
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Sculley also saw greater potential in Google.
"I think where Google really has a long run ahead of them is with their ability to do big data analytics in the cloud," he said. "They're probably further ahead than Apple, even further ahead than Amazon in many ways, further ahead than Facebook.
"And they haven't really tapped all the things they can do, and yet they've got an incredible cash flow from their advertising business, which enables them to invest in new areas, speculate on things that other people just don't have the resources to do. I see Google as being a play for the long term."