Murray was speaking after he beat Ivo Karlovic to reach the Wimbledon quarter-finals for the eighth successive year.
Kyrgios has been making headlines with his poor behaviour throughout the tournament in London.
His fourth round exit this week - where he was accused of tanking - prompted Australian swimming great Dawn Fraser to say that he and fellow Australian Bernard Tomic should "go back to where their parents came from."
Fraser has since "unreservedly apologised" for her comments, while Kyrgios has accused her of blatant racism.
Murray has been in the spotlight from a very early age and he has constantly had to shoulder the weight of expectation from the British public.
In 2013, he became the first British man to win the men's singles title at Wimbledon since Fred Perry won in 1936.
Kyrgios, 20, has angered tennis fans at Wimbledon with his antics, but Murray sympathises with what the Australian is going through.
"I don't think people appreciate how difficult it is to grow up under the spotlight, how difficult it is to have loads of people expecting you to be perfect from a young age," Murray said.
"I like Nick. I've spoken to him away from the court. He's quite different to how he is on it.
"It's not easy. He'll find his way, for sure. He'll hopefully have good people around him that can help him, people that have experienced being on the tour, guys like Lleyton Hewitt and Pat Rafter."
Murray will play Canadian Vasek Pospisil in his quarter-final on Wednesday.
