Speaking to The Guardian newspaper, Nick Clegg said Putin was applying "yesterday's divisions and arguments to today's problems".
Clegg acknowledged there was a "pronounced Russian imprint" in the Crimean peninsula which meant it could not be viewed the same way as other parts of Ukraine.
The British deputy premier urged Putin to engage in a "civilised discussion" with the new government in Kiev.
"Putin's reaction is very revealing. It's as if he's been in a sort of deep freeze since the Cold War and hasn't moved with the times," Clegg said.
Former KGB spy Putin headed its successor, the Federal Security Service, shortly before he first became president in 2000.
"He gives every appearance of applying a KGB mentality rooted in the Cold War to new realities in 21st-century Europe," Clegg said.
"To regard closer ties between Ukraine and a non-military organisation like the European Union as the equivalent to American tanks on your lawn at the height of the Cold War suggests to me that we're dealing with a man who's applying yesterday's divisions and arguments to today's problems."
Clegg acknowledged Moscow's special links to Crimea, which was transferred from Russia to Ukraine in 1954 when they were both in the Soviet Union.
"Crimea already has a semi-autonomous status within Ukraine and clearly has a different history to other parts of Ukraine and has a very pronounced Russian imprint on it, not least because of the presence of the Russian Black Sea naval operation," which is based there, said Clegg.
"So it is already in a different category and I don't think anyone wants to deny that.
"No one is somehow suggesting that Crimea should be treated exactly the same as other parts of Ukraine given that it hasn't been treated like that in the past by the Ukrainians themselves."
British Prime Minister David Cameron has said Russia's actions in Crimea have been "completely unacceptable", echoing statements made by other European leaders and US President Barack Obama since Moscow took de facto control of the peninsula in the wake of pro-Russian president Viktor Yanukovych's ouster two weeks ago.