"I was disappointed because, you know, even though we don't have an extradition treaty with them, traditionally we have tried to respect if there's a law breaker or alleged law breaker in their country, we evaluate it, and we try to work with them," Obama told NBC channel in an interview.
Snowden, a former NSA contractor, is accused of leaking details about highly-secretive government surveillance programmes. The US wanted Russia to hand over Snowden to face trial for unauthorised leaking of highly classified information. Russia, however, grated him temporary asylum.
"They didn't do that with us, and in some ways it's reflective of some underlying challenges that we've had with Russia lately. A lot of what's been going on hasn't been major breaks in the relationship. They still help us on supplying our troops in Afghanistan. They're still helping us on counter-terrorism work," he said.
Obama, however, said he would be travelling to Russia later this year to attend the G-20 Summit.
"I will be going there (to Russia). I will be going to that because the G20 Summit is the main forum where we talk about the economy, the world economy with all the top economic powers in the world. So it's not something unique to Russia.
They are hosting it this year," he said.
"It's important for us as the leading economy in the world to make sure that we're there. In part because we're creating jobs, improving our economy, building up our manufacturing base, increasing wages. All those things now depend on how we compete in this global economy. And when you've got problems in Europe or China is slowing down, that has impact here in United States," he said.
Russians, Obama said, were helpful after the Boston bombing in that investigation.
"So there's still a lot of business we can do with them.
But there have been times where they slip back into Cold War thinking and a Cold War mentality, and what I consistently say to them and what I say to President Putin is that's the past, and we've got to think about the future, and there's no reason why we shouldn't be able to cooperate more effectively than we do," he said.
In the wake of the Snowden episode, Obama said his administration is trying to reduce dependence on contractors.