Richard Parsons, who chaired the Citigroup Inc board that lost a shareholder vote this week on executive compensation, said on Thursday that directors had failed to adequately explain to investors the methods they used to determine pay packages.

At Citi's annual meeting on Tuesday, only 45 percent of shareholders endorsed the pay plan in an advisory vote required under the 2010 Dodd-Frank financial oversight law.

Under Parsons' chairmanship, the Citigroup board paid CEO Vikram Pandit $15 million in 2011. Outside proxy advisory firms used by institutional investors had criticized the pay plans for leaving too much room for director discretion and not adhering closely to measurements of Pandit's performance.

The say on pay vote was non-binding, but it was an embarrassing rebuke for the bank by its investors.

In an interview on Thursday, Parsons said he believes the issue can be dealt with through better communication. Parsons, who became chairman in 2009, announced in March that he would retire from the board after the meeting.

I'm certain that the new board and the comp committee will engage in serious discussion with the representatives of the shareholders, particularly the institutional ones, and that this will not be a problem going forward, he said in Washington on the sidelines of an event hosted by the Rockefeller Foundation, a philanthropic organization.

The issue, according to Parsons, is shareholders' desire to have pay packages tied to very specific metrics.

The former chairman said the board should have done a better job explaining that it was using specific criteria to determine compensation.

I think we actually had a more quantitative approach. We just didn't adequately connect it up with their sense of the quantitative, he said.

Among other complaints, proxy advisory firms objected that the board decided in 2011 to give Pandit a retention award of $34.4 million over three years that depends in part on whether the company has a culture focused on responsible finance.

The award also depends on whether the company's Citicorp division earns over two years $12 billion before taxes.

By using a dollar amount as the test, the board left the chance that Pandit will get the award based on the performance of the economy rather than his own work, advisory firm Glass, Lewis & Co said.

Earlier on Thursday during a discussion at the Rockefeller event, Parsons cautioned about being too prescriptive in how executive pay packages are awarded.

You can't just throw a formula up against the wall because then you have managers managing to the formula as opposed to what the business needs, he said in response to a question from the audience.

On Thursday, Representative Barney Frank, an author of the 2010 law, heralded the Citi vote and said he believes it will encourage shareholders of other companies.

The result should be a reduction in the excessive levels of compensation to financial company executives that will leave them still extremely well compensated, but not as poster children for unfairness in our country, Frank said in a statement.

(Reporting By Dave Clarke in Washington and David Henry in New York; editing by Andre Grenon)