Klitschko, the brother of opposition leader Vitali Klitschko, is training in Florida for his title defense in April. He sat before a Ukrainian flag at a press conference, wearing a white T-shirt with his country's name and logo.
"You cannot repeat the mistakes of history, and there were a lot of mistakes," Klitschko said when asked about a message to Putin.
Klitschko said he feels sadness about the months of protests and sporadic violence in his country, and his "mind is over there, my body is here."
Russian forces effectively took control of Crimea about two weeks ago after the ouster of Ukraine's pro-Russia president, Viktor Yanukovych. Klitschko's brother gave up boxing to run for president in the Ukraine, where elections are scheduled for May 25.
"He's representing me in a certain way over there, and I'm representing him in a certain way over here," said Klitschko, who speaks with his brother daily. "But I know, as Nelson Mandela said, 'Sport has the power to change the world.' And I believe in that very strongly."
Klitschko stressed there was only one path to peace.
"There's only one solution. There is, by no means, no way, a military solution," he said. "It's all about diplomacy and good politics because nobody can return the lost loves.
"I just hope with all the international presence and awareness, certain steps from the political and diplomatic side will put the legal question into place."
Klitschko suggested Russia's takeover of Crimea could happen elsewhere.
"Geo-politics is a very sensitive topic," he said. "If you think about it, with all the quality of the lawyers, they could find out the deal between Russia and the United States that was made with Alaska there were some loopholes in the contract.
Klitschko, who turns 38 on Tuesday, spoke after a workout for his April 26 title defense against Alex Leapai in Germany. He plans to travel to Austria on Saturday for more training and return to Ukraine after the fight.
He said his athletic career helps him deal with the crisis in his homeland.
"It's disappointment, it's anger, it's being worried. It's a combination of all, you can imagine," he said. "There's a lot of emotions, but I understand. It's like in a boxing match, if you get too emotional, you're definitely going to produce mistakes that are eventually going to cause more damage."
Klitschko said the crisis began when the people of Ukraine got tired of "the regime, the dictatorship" of Yanukovych and not because of Western intervention.
"It's frustrating because, not just myself, but no one could have imagined something like that could happen," he said. "It was just something impossible in a country such as the Ukraine, which was never involved in any war, never had any terrorist attacks. A country that always was open and welcome, as we saw for the European soccer cup, which we shared with Poland.
"I wish that we're going to pass this process in a positive and good way and with a good solution as soon as possible. Thankfully, the European Union and the United States are really aware of what's going on in the Ukraine from the beginning."