By Michelle Nichols

UNITED NATIONS (Reuters) - Russia failed to win re-election to the United Nations Human Rights Council on Friday, beaten out by Hungary and Croatia, following lobbying by rights groups against Moscow's candidacy because of its military support for the Syrian government.

In a secret ballot by the 193-member U.N. General Assembly, Hungary received 144 votes, followed by Croatia with 114 votes and Russia with 112 votes. Russian U.N. Ambassador Vitaly Churkin said Moscow had faced good competition.

"It was a very close vote," Churkin told reporters. "Croatia, Hungary - they are fortunate because of their size they are not as exposed to the winds of international diplomacy; Russia is quite exposed."

"We have been there a number of years, I'm sure next time we're going to get in," he said.

Russian air power has been backing Syrian President Bashar al-Assad's forces in the country's nearly six-year war. A recent offensive to capture eastern Aleppo - the rebel-held half of Syria's largest city - has sparked international outrage.

Russia's three-year term on the 47-member Geneva-based Human Rights Council will finish on Dec. 31. It had been competing for a second three-year term. Council members cannot serve more than two consecutive terms.

"U.N. member states have sent a strong message to the Kremlin about its support for a regime that has perpetrated so much atrocity in Syria," said Louis Charbonneau, U.N. director at Human Rights Watch.

The United States, Egypt, Rwanda, Tunisia, Iraq and Japan were elected to the body, while Saudi Arabia, China, South Africa and Britain won a second terms. Their candidacies were uncontested but needed to win a majority vote. In the other competitive slate, Cuba and Brazil beat out Guatemala.

"The re-election of China, Cuba and Saudi Arabia - regimes which systematically violate the human rights of their citizens - casts a shadow upon the reputation of the United Nations," said U.N. Watch Executive Director Hillel Neuer."

A Saudi Arabia-led military campaign in Yemen has been criticized for killing civilians. U.N. sanctions monitors have accused the Saudi-led coalition, Houthi rebels and Yemen government troops of violating international humanitarian and human rights laws.

(Editing by Steve Orlofsky)