The Journal, however, says Buffett shared his concerns privately with Coke CEO Muhtar Kent in three conversations in recent weeks, including a dinner in Omaha.
Buffett told the newspaper, "I'm against the plan, and they know it," calling his abstention "just as clear as voting no, in my view."
Activist investor David Winters, a vocal opponent of the pay plan due to fears it would excessively dilute the holdings of current shareholders, complained that Buffett had not "seized the opportunity" to speak out before the vote.
Read MoreBuffett: I've voted for bad pay plans
Buffett told the Journal that while Winters "is right about the fact that it's excessive," he's wrong about the extent of the dilution, "which is another reason not to join him."
The Journal reports that a Coke spokesman said in a statement, "No changes are being made to the plan at this time," while also noting it has the "maximum flexibility" to "ensure that it continues to meet the needs of the business and remains in line with all shareowner interests."
—By CNBC's Alex Crippen. Follow him on Twitter: