Andrei Sizov, a 47-year-old owner of a nearby wood workshop, said the strikes came at night.
"Around 1.30am, my security guard called me because there was an airstrike," he told AFP.
"There were five hits. My employee was in the office and got thrown off his feet by the blast. They are making us pay for destroying the Moskva."
After the attack on the Moskva on Thursday, the Kremlin initially said its weaponry was not damaged and it was en route back to its home base at Sevastopol, in Russian-occupied Crimea.
But later on Thursday, the Russian defence ministry admitted the loss in a statement that said: "While being towed towards the destined port, the Moskva cruiser lost its balance due to damage sustained in the hull as fire broke out after ammunition exploded. The vessel sank due to the choppy seas."
The ministry later said all the crew, thought to be around 500, had been evacuated.
But Ukraine on Friday claimed the ship's captain, commander of the Black Sea Fleet Anton Kuprin, died during the explosion and ensuing fire on board.
A senior US official said Washington also believed there were Russian casualties, though the numbers were unclear.
Ukraine said it was braced for further retaliation. "The Moskva cruiser strike hit not only the ship itself – it hit the enemy's imperial ambitions," Natalia Gumeniuk, a spokesman for Ukraine's southern military forces, said on Friday.
"We are all aware that we will not be forgiven for this. We are aware that attacks against us will intensify and that the enemy will take revenge."
"We saw that other ships tried to assist it [the Moskva], but even the forces of nature were on Ukraine's side because the storm made both the rescue operation and crew evacuations impossible."
Mikhail Razvozzhayev, the governor of Sevastopol, on Friday described the sinking as a personal loss, writing on social media: "The cruise was a true symbol of our city, and we all feel the pain today. Rest in peace, Great Ship."
Several dozen people gathered at a war memorial in Sevastopol to commemorate the ship on Friday afternoon. A funeral wreath with "the Moskva" emblazoned on it was placed at a monument marking the 300th anniversary of the Russian navy.
A Kremlin spokesman on Friday rejected suggestions Vladimir Putin should visit Sevastopol to oversee the investigation into the attack on the Moskva, calling it a matter for the defence ministry.
The vessel was inaugurated in 1983 under the name Slava before being renamed Moskva in 1996 and has played a major role in Russian military campaigns.
Most recently, the Moskva was involved in the operation against Ukraine's Snake Island, in the Black Sea, in the first days of the war, when it called Ukrainian soldiers to surrender. In a widely circulated recording, a Ukrainian soldier replied: "Russian warship, go f*** yourself."
Russian pundits called for more airstrikes on Ukraine in response to the sinking.
"The Moskva is an absolute reason for an all-out war, 100 per cent," Vladimir Bortko, the film director, said on a news talk show on Thursday.
But Igor Girkin, a retired Russian officer who led separatist rebels against the Ukrainian government at the start of the 2014 war in the east of the country, posted a sarcastic statement that said: "Who at our General Staff could imagine the Ukrainians would fire in response?"
Ukrainian officials have been quick to gloat over the incident. Oleksii Reznikov, the Ukrainian defence minister, wrote on Twitter that the wreck would make an excellent site for divers.
"We have one more diving spot in the Black Sea now," he added. "Will definitely visit the wreck after our victory in the war."
