Fallon's remarks were made Wednesday as UK warships and warplanes tracked Russia's only aircraft carrier through the English Channel.
The carrier and its escort, the guided missile cruiser Petr Velikiy, are on their way back to Russia after participating in airstrikes in Syria. They left the Mediterranean Sea earlier this month
"We are keeping a close eye on the Admiral Kuznetsov as it skulks back to Russia, a ship of shame whose mission has only extended the suffering of the Syrian people," Fallon said.
The Russian Defense Ministry said in a statement it had "paid attention" to Fallon's remarks on the carrier group.
"The Russian combat ships do not need escort services," the statement said. "They know the fairway and the course."
The ministry also suggested Fallon should be "paying more attention to the British fleet."
Johnson: Russia's peace efforts 'a plus'
UK Foreign Secretary Boris Johnson struck a slightly different tone to his defense counterpart Thursday, noting Moscow's role in bringing about Syrian peace talks
in Astana, Kazakhstan, this week, following on from its military involvement.
"To the extent that the Russians are capable of getting a ceasefire and stopping suffering, that must be rated a plus," Johnson told a House of Lords committee.
"That comes, of course, after a pretty brutal and barbaric bombardment of Aleppo and other places which they facilitated -- or, I'm sure, perhaps even participated in," he said.
Johnson said Russia had intervened in Syria "to considerable effect" by preserving the regime of Syrian President Bashar al-Assad and described its involvement there as a "fact of life" after other powers, such as Britain, had declined to step in.
Russia's airstrikes in support of Assad's forces have been crucial in helping them gain the upper hand in the long-running conflict.
In December, they succeeded in pushing rebel fighters from the key city of Aleppo.
Syria's brutal civil war has raged on for nearly six years and killed an estimated 400,000 people.
'Show of force'
British forces also shadowed the Russian carrier group in October on its way to Syria.
At the time, Russia said the Kuznetsov's voyage was "to ensure naval presence in the important areas of the world ocean. Special focus will be made on safeguarding security of maritime traffic and other types of Russian maritime economic activity and also responding to new kinds of modern threats such as piracy and international terrorism."
But others took a different view.
"It's a show of force and a show of capabilities," Peter Felstead, editor of Jane's Defence Weekly, told CNN in October. "In terms of strike missions, they (the Russians) could just as easily have conducted them with the land-based aircraft they already have in Syria."