"Putin fears no retribution" from the United States, said the Texas Republican in an interview shown Sunday on ABC's "This Week."
Cruz, who called Putin a "KGB thug," said the Obama administration's policy has been to "alienate and abandon" U.S. allies and to "coddle and appease our enemies."
"You better believe Putin sees in Benghazi [Libya], four Americans are murdered and nothing happens, there's no retribution," he said. "You better believe that Putin sees that in Syria, Obama draws a red line and ignores the red line."
Cruz said the president was wrong not to "stand unapologetically, emphatically" in support of Ukrainian protests last month that eventually led to the ouster of former President Viktor Yanukovych.
"When the United States doesn't speak for freedom, tyrants notice," he said.
The Texan and Tea Party favorite stopped short of calling for American troops to become directly involved in the Russia-Ukraine conflict but said the U.S. "absolutely" should impose sanctions on Russia in response to its invasion of Crimea.
"There are a host of things we can do," he said.
"I'm a big fan of Rand Paul, he and I are good friends; I don't agree with him on foreign policy," he said.
Paul says he is considering a run for president in 2016, and there is widespread speculation Cruz also will run.