A three-judge panel of the court in Moscow ruled that his sentence should remain "unchanged", Russian news agencies reported.
Supporters of Sentsov attending the hearing reacted defiantly to the verdict, shouting "Ukraine will win" and "Glory to Ukraine! Glory to the heroes", according to video shot by Ukrainski Novini news agency.
Some were dressed in the yellow and blue colours of the Ukrainian flag.
Sentsov and his co-defendant in the case, Alexander Kolchenko, followed the proceedings by video link from a prison in the southern city of Rostov-on-Don.
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Russia found Sentsov guilty in August of founding an extremist group linked to Ukraine's Pravy Sektor (Right Sector) ultra-nationalists that carried out several arson attacks and planned other attacks in the Crimea peninsula annexed by Moscow.
Sentsov denied the charges. His alleged collaborator Kolchenko also received a 10-year term.
World-famous filmmakers, including Germany's Wim Wenders, had expressed outrage over the director's imprisonment and appealed for his release.
Defence lawyers said the men were tortured and threatened during the investigation.
Their trial was decried as "fatally flawed" by Amnesty International, while the EU said it breached international law and the US called it a "clear miscarriage of justice."
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Sentsov's debut film Gamer about a computer-game obsessed teenager was shown at the Rotterdam Film Festival in 2012.
He was working on a second film when he was detained by Russian special forces in May 2014 after taking part in protests against Russia's annexation of his home region of Crimea from Ukraine two months earlier.
Asked if he wanted to address the court on Tuesday, Sentsov said "there's nothing more to talk about."
The defence team said they would push for the men to be released as part of a prisoner exchange between Russia and Ukraine.
"We will work on resolving the question of an exchange," said Sentsov's lawyer Dmitry Dinze, quoted by Interfax news agency.
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