While there was no risk of starting World War Three, he said, he believed it was part of an attempt to set up military bases in or near Ukraine.
President Putin alleged a US spy plane was part of the operation too.
The Royal Navy rejected the Russian account of what happened on 23 June.
BBC correspondent Jonathan Beale, on board HMS Defender at the time, said it had been buzzed by Russian warplanes and coastguard vessels had threatened to open fire on the ship. While some firing had taken place, he said it was well out of range.
Reiterating the navy's explanation, Prime Minister Boris Johnson's spokesman said on Wednesday that the destroyer "was conducting innocent passage through Ukrainian territorial waters in accordance with international law".
A separate encounter in the Black Sea has since been reported the following day by the Dutch navy, which has accused Russian fighter jets of repeatedly harassing its ship, HNLMS Evertsen.
After last week's incident involving HMS Defender, the British ambassador was summoned by the Russian foreign ministry, which protested against what it said was a violation of its territory. Crimea was seized by Russia in 2014 but most of the international community considers it to be part of Ukraine.
Classified UK documents assessing Russia's likely response have since been found dumped near a bus stop in Kent, in south-east England.
Asked during his annual TV phone-in with Russian citizens whether the incident risked provoking World War Three, the Russian president said even if HMS Defender had been sunk that would not have happened.
"They know they cannot win this conflict: we would be fighting for our own territory; we didn't travel thousands of miles to get to their borders, they did," he said.
However, he did accuse the UK and the US of mounting a co-ordinated, provocative operation to assess Russia's response.
Mr Putin pointed out he had personally ordered troops to pull back from Ukraine's borders two months ago, as international concern intensified over what Russia insisted was nothing more than military exercises.
Now he said that British and US forces were trying to open up military bases, "making Ukrainian territory close or on the border with Russia a military platform that is a threat to Russian security". He also linked it to his summit with President Joe Biden in Geneva the week before.
He suggested that a US reconnaissance plane had taken off from a Nato airfield in Greece, possibly from Crete.
However, he did not mention Dutch naval accusations that Russian warplanes armed with missiles had flown dangerously low, staging "mock attacks" on the frigate HNLMS Evertsen south-east of Crimea.
Dutch Defence Minister Ank Bijleveld insisted the ship had every right to sail there and there was no justification for "this kind of aggressive action that unnecessarily heightens the risk of accidents".
The Russian defence ministry has since said that Su-30 fighters and Su-24 bombers were scrambled and carried out flights "at a safe distance" from the ship.
President Putin has made clear he blames Nato and its expansion for the conflict in eastern Ukraine which erupted in 2014. Russian-backed separatists took control of large areas of the east after Moscow seized Crimea.
But Mr Putin wrote in an article published last week that the US had organised a coup in Ukraine and Europe had actively supported it.