But the United States will have to "step up our game," the president said.
Speaking to reporters aboard Air Force One, Obama said of his extensive Asian trip, "No. 1, I think all of Asia is eager for American engagement and leadership. We saw that in India; we saw it in Indonesia; we saw it in -- during the G20 (in Seoul) and we saw it during APEC (the Asian-Pacific Economic Cooperation summit in Japan).
"And it wasn't just from leaders," he added. "I was struck when I was at the first school that we went to in Mumbai, and those young kids who were talking about the environment and green technology. On the way down, I said, 'Well, what are you guys' plans?' 'Well, we're of course going to go to college.' I said, Where are you going to go?' 'Well, America, of course.'"
The president said Asia is on the move.
"Korea, China, India, the entire Southeast Asian region -- Japan -- all of them recognize how competitive things are and that they are thinking each and every day about how to educate their workforce, rebuild their infrastructure, enter into new markets," he said. "And we should feel confident about our ability to compete, but we are going to have to step up our game."
Facing a Republican takeover of Congress in January, Obama said he expected some compromises in the lame duck session, as well as some movement on taxes and a new START treaty.
Republicans, he said, "are flush with victory after a campaign of just saying no. But I'm sure the American people did not vote for more gridlock."