Carney told reporters he believed that Obama addressed the issue "very thoughtfully."
"As a longtime Redskins fan and Washingtonian, I really appreciate what he had to say," he added.
In an interview with the Associated Press on Saturday, Obama said he would be open to changing the team name if he was their owner.
"If I were the owner of the team and I knew that the name of my team — even if they've had a storied history — was offending a sizable group of people, I'd think about changing it," the president swayed.
Native American groups say the nickname is offensive, but the team owner Daniel Snyder has said he has no intention of changing it.
Carney said he did not believe Obama had spoken to Snyder about the issue.
White House correspondent Brian Hughes contributed to this report.