WASHINGTON—Federal Reserve Vice Chairwoman Janet Yellen, in her Senate confirmation hearing for the central bank's top post, said addressing the "too-big-to-fail" problem is "among the most important goals of the post-crisis era."

In the question-and-answer portion of her hearing before the Senate Banking Committee on Thursday, Ms. Yellen also said that while the economy has gotten stronger since the financial crisis, the recovery still needs help from the Fed.