"I made it clear that I would be willing to serve, so yes, I do feel a sense of disappointment" about not being renominated, Yellen said. The only woman to serve as the head of the US central bank described her work at the Fed as "the core of my existence".
Yellen said she's supportive of former investment banker Powell, 64, whom she termed "thoughtful, balanced and dedicated to public service".
The financial system was now "much better capitalised" and the banking system "more resilient" than they were entering the global financial crisis a decade ago, Yellen said.
"What we look at is, if stock prices or asset prices more generally were to fall, what would that mean for the economy as a whole?" Yellen said. "And I think our overall judgment is that, if there were to be a decline in asset valuations, it would not damage unduly the core of our financial system."
Yellen's final act at the Fed was to hit one of the largest US banks, Wells Fargo & Co, with an unusual ban on growth that follows the San Francisco-based lender's pattern of consumer abuses and compliance lapses.
In the interview, she warned that it would be a "grave mistake" to roll back the regulations put on banks after the previous economic collapse.
The current US economic expansion is now approaching nine years and is the third longest in duration since 1945, according to the National Bureau of Economic Research. Yellen said the economy can continue to grow.
"Yes, it can keep going," she said. "Recoveries don't die of old age."