Carlyle Group’s first-quarter income dropped 26 percent, the Washington-based firm said Tuesday in its first earnings report since its lukewarm debut on the public stock markets.

Shares of the company, which went public May 3, eked out a 0.4 percent gain in regular trading Tuesday to close at $21.12, below the initial public offering price of $22 a share.

In a call with investors, Carlyle co-founder David Rubenstein said the earnings report was “in line with expectations prior to going public.” He emphasized that Carlyle, the largest private equity firm in the world, focuses on long-term results, holding investments for four or five years.

“We would encourage those who choose to follow us not to focus disproportionately on quarter-to-quarter results,” he said. “Instead, we encourage a longer-term perspective.”

The company’s results are based on “economic net income,” a measure — common within the private equity industry — that includes unrealized gains. Because of lower performance fees, that income fell to $392 million from $533 million in the first quarter of 2011.

The private equity industry has generated recent media attention since Mitt Romney, a founder of the private equity firm Bain Capital, emerged as the likely GOP presidential candidate.

But on Wall Street, investors seem to shrug at private equity stocks. Shares of Blackstone Group, another major private equity firm, launched at $31 in 2007. Tuesday, they closed at $12.19.

Carlyle faced some difficulty wooing investors, debuting with a share price slightly lower than initially projected. It sold 30.5 million units at $22 apiece, slightly lower than the $23-to-$25 valuation that had been expected.

Rubenstein is a well-known Washington philanthropist who has made investments in repairing the Washington Monument after the 2011 earthquake and funding the panda research program at the National Zoo. He purchased a 1297 copy of the Magna Carta for $21.3 million in 2007 and has it on permanent loan to the National Archives.

In Tuesday’s investor call, Rubenstein noted that the Carlyle Group brought in $2.8 billion in fundraising in the first quarter, indicating that the “fundraising environment appears to be gaining momentum” after slowing during the recession.