Clinton attended the ceremony unveiling the statue at Moscow State University with Russian officials including Moscow Mayor Yuri Luzhkov, an outspoken foe of gay rights. She made no mention of the issue during the ceremony.
Luzhkov has blocked all attempts to hold gay pride marches in Moscow, once saying gay pride parades "can be described in no other way than as satanic."
Whitman is claimed by the gay and lesbian communities in the U.S. as one of their own.
Gay activist Nikolai Alexeyev said Wednesday he was disappointed Clinton did not discuss discrimination against gays during her time in Moscow. "Russia is supposed to be a democracy and she said nothing," he said.
Alexeyev had called on Clinton to denounce what he called entrenched and degrading homophobic attitudes in Russia at a news conference Tuesday.
A U.S. state department spokesman said the department was unaware of any request from the Russian gay community.
Homosexuality was only decriminalized in Russia in 1993 and homophobic attitudes remain widespread.
Activists have taken the struggle to hold a gay pride parade in Moscow to the European Court of Justice, which is scheduled to rule on the issue in early 2010.
The statue of Walt Whitman was placed in the gardens of Moscow State University, where in May more than 30 gay activists were arrested for attempting to hold a pride march.
Among those detained was prominent British human rights campaigner Peter Tatchell.
A representative of the American-Russian Cultural Cooperation Foundation, which organized the statue's emplacement, distanced the group from the gay rights issue on Tuesday.
"Whitman transcended his sexuality in his art and I would like to thank Mayor Luzhkov for welcoming him in his city and have absolutely nothing to say about those things," said foundation representative James W. Symington, a former four-time congressman for Missouri. He was in Moscow for the ceremony.
The statue of Walt Whitman will complement a statue of the Russian poet Alexander Pushkin installed in Washington in 2000.
The sculptor Alexander Bourganov remarked at a press conference Tuesday that the opening had been delayed and been politically difficult. He did not elaborate.
Associated Press Writer Matthew Lee contributed to this story.