Coca-Cola said 83 per cent of shareholders approved the plan. Critics, however, said the plan would dilute the holdings of current shareholders too much.
As of December 31, Berkshire owned 400 million shares of the company, just over 9 per cent of the shares outstanding.
Buffett said he and partner Charlie Munger did not want to vote against the plan because he did not want to show disapproval of management, adding that he has enormous respect for Coca-Cola's chief executive, Muhtar Kent.
"I love Coke, I love the management, I love the directors, so I didn't want to vote 'No,'" Buffett said. "It's kind of un-American to vote 'No' at a Coke meeting. I didn't want to express any disapproval of management but we did disapprove of the plan. The plan compared to past plans was a significant change."
Buffett said he has no intention of selling any Coca-Cola shares.
The Coca-Cola board of directors "respects Mr. Buffett's philosophical stance on equity-based compensation," the board said in a statement.
"We greatly respect his views and look forward to continuing our productive relationship with him for many years to come," the statement added.
Nonetheless, Buffett said that investor activism is getting stronger.
"The CEOs are terrified of activists. I can tell you that," Buffett said. "They are all talking to investment bankers and lawyers and saying, 'What do we do about this?'"
He denied he had soured on his enormous investment in IBM, and said Berkshire bought some more shares this year, although the purchases did not come after IBM's most recent earnings report. He said he would not rule out future IBM stock buys.
Buffett also said that safety is a major priority for the rail industry, after a recent spate of accidents raised concerns about how to transport oil safely.
"I can tell you that's all they're thinking about," the investor said in an interview with Reuters.
"We're going to move a lot of crude in this country, and we have to learn how to do it very safely," he added.
He added that the delay in the construction of the Keystone pipeline was unlikely to prompt additional purchases of tank cars at Berkshire railroad unit BNSF.
Earlier this year the railroad said it plans to buy its own fleet of up to 5,000 new crude oil tank cars with safety features that exceed the latest industry standards.
Oil by rail has surged in recent years, helped by a boom in North Dakota. Traffic is now running 10 per cent ahead of last year at this time, with BNSF accounting for roughly a third of US oil-by-rail traffic.
But recent accidents have underscored the dangers of transporting the volatile fuel by train, with Canada now planning to phase out older tank cars to improve safety.
Buffett was in New York for lunch with an anonymous bidder who paid $1,000,100 to win last year's "Power Lunch with Warren Buffett" auction benefiting San Francisco's Glide Foundation.
His New York visit comes ahead of the company's annual meeting in Omaha, Nebraska, on May 3. Tens of thousands of people flock to the gathering every year to hear Buffett and Munger answer hours of questions about the company's future.