Speaking to reporters on Air Force One, White House press secretary Josh Earnest said the President recognises the emotional nature of presidential campaigns.
"The President certainly understands the emotions and personal investment that's required to mount a campaign," Earnest said. "So the President's respectful of that personal investment and again when you have performed as well as Senator Sanders has, he certainly exceeded everybody's expectations, possibly even his own, in terms of the support and enthusiasm that he would generate and carry all across the country, he's earned the opportunity to make these decisions based on his own thinking and based on his own schedule."
Speaking to Fallon in front of a packed audience, Obama observed that any fierce battle for a presidential nomination is bound to create some tension.
"And what happens during primaries [is] you get a little ouchy, Everybody does," he said.
"So there's a natural process of everybody recognising that this is not about any individual but this is about the country and the direction we want to take it."
Obama said he has spoken to both Clinton and Sanders "at some points" during the campaign. "I don't know if they asked me for advice, but I give it anyway," he said.
Fallon asked whether the GOP presumptive nominee, Donald Trump, had called the President for advice, to which Obama gave a one-word answer: "No."
"But do you think the Republicans are - happy with their choice?" Fallon mused.
"We are. But I don't know how they're - I don't know how they're feeling," Obama replied, prompting a cheer from the audience, before adding, "that was too easy. But the truth is actually I am worried about the Republican Party."
The President said that while there "are wonderful Republicans out in the country who want what's best for the country," the current GOP leadership does not reflect that.
"But what's happened in that party culminating in this current nomination, I think is not actually good for the country as a whole," he said.
"It's not something Democrats should wish for. And my hope is, is that maybe once you get through this cycle, there's some corrective action and they get back to being a centre-right party. And Democratic Party being a centre-left party. And we start figurin' how to work together."