"This office has a way of waking you up," he told reporters before heading out for his final scheduled foreign trip before he leaves office.
"There is enormous continuity beneath the day-to-day news that makes us that indispensable nation when it comes to maintaining order and promoting prosperity around the world," he said. "That will continue."
"Do I have concerns?" he asked rhetorically. "Absolutely."
But Obama said when he met with the president-elect at the White House last week, Trump "expressed a great interest in maintaining our core strategic relationships," including NATO, to which Trump previously hinted he would move the U.S. away from if allies do not pay their "fair share".
Broadly speaking, Obama said he thinks that Trump is ultimately pragmatic and not an ideologue.
"And that can serve him well as long as he has got good people around him and he has a clear sense of direction," he said.
Obama acknowledged that there are "deeply disaffected" people in the U.S. that helped to propel Trump to the Oval Office, but said the country he is passing on to Trump is far better than the one he inherited from George W. Bush.
"The incoming administration doesn't have to put out a huge number of fires," he said. "They may want to take the country in a significantly different direction. But they have got time to consider what exactly they want to achieve."
Asked about Trump's appointment of white nationalist Stephen Bannon to be his senior counselor, Obama declined to comment directly, but said "it's important for us to let him make his decisions.
"The American people will judge, over the course of the next couple of years, whether they like what they see and whether these are the kinds of policies and this is the direction that they want to see the country going," he said.
Moving to the Iran nuclear agreement, Obama said the deal is "working" and Iran is complying with its obligations.
Trump has threatened to tear up the agreement on the first day of his presidency, but Obama said if he were to do so it could alienate the U.S. in the international order, particularly among some of its closest allies.
"When you're not responsible for it, I think you can call it a terrible deal. When you are responsible for the deal and preventing Iran from getting a nuclear weapon, you're more likely to look at the facts," he said.
"For us to pull out would then require us to start sanctioning those other countries in Europe or China or Russia, that were still abiding by the deal, because from their perspective, Iran had done what it was supposed to do," he added.
And on Syria, Obama acknowledged that his policies have "not worked", and he contemplates his failures there "every day".