After Donald Trump’s victory in 2016, I predicted that Russia’s stance toward the U.S. would become more antagonistic. Vladimir Putin always needs a foreign enemy to rally his nation around him and divert attention from the poor Russian economy. Mr. Putin’s aggression has indeed managed to raise tension between the U.S. and Russia. But instead of reinforcing Mr. Putin’s narrative by punishing Russia as a whole, the U.S. should target its response toward Mr. Putin and his inner circle.

Mr. Putin’s conflicts with the U.S. are...