Some of America's biggest and brightest investors can admit to making mistakes in the stock market from time to time.

"We mishandled Apple," Omega Advisors' Leon Cooperman told CNBC on Wednesday.

Cooperman, who has a position in Microsoft, told CNBC's "Halftime Report" that his firm sold stock in Apple "early" because they were concerned about competition. "We were wrong," he admitted.



That being said, the hedge fund manager said he has seen some of his other bets in the tech sector pay off, Alphabet being one example.

"[Alphabet] is sitting on a fortress balance sheet," Cooperman said. But nevertheless he thinks it should follow the lead of one of its big tech rivals.

"We think [Alphabet] should take a [page] out of Apple's book ... and more aggressively deploy cash, which turned out to be a good decision" for Chief Executive Tim Cook and his team. Nevertheless, Larry Page's internet search company is generating substantial free cash flow and "makes sense" for many investors today, Cooperman said.

When it comes to social media, the chief executive of Omega Advisors likes Facebook more than anything else — again because of its "fortress balance sheet."

"[Facebook] has a dominant position in what they do," Cooperman told CNBC. "There's no secret sauce."

Success comes as a result of a combination of a high trading multiple, growth in the equity and how secure the company's industry position is, Cooperman added. "We're looking for value and we find value in many places. ... That's what investing is all about."

As of Wednesday afternoon, Apple has gained more than 30 percent over the past 12 months, Alphabet is up close to 13 percent, and Facebook has climbed a little more than 27 percent.