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.
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"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.
"So it is already in a different category and I don't think anyone wants to deny that.