"What does that do to our standing in the world community?" he asked in remarks on the Senate floor.
Although he had made no secret of his hope to retire by now, Panetta will be back in the Pentagon next week.
His press secretary, George Little, said Panetta will fly to Brussels for a NATO meeting late next week where allies will consider the size and scope of a post-combat mission in Afghanistan. The U.S. is hoping allied nations will contribute troops and money for continued training of Afghan security forces, which are to be fully responsible for security by the end of 2014.
Obama himself suggested that Hagel's absence from the Brussels meeting could hurt the war effort. He also criticized Republicans for blocking the Hagel nomination and forcing him to win 60 votes instead of the usual majority.
"It's just unfortunate that this kind of politics intrudes at a time when I'm still presiding over a war in Afghanistan, and I need a secretary of defense who is coordinating with our allies to make sure that our troops are getting the kind of strategy and mission that they deserve," the president said in an online chat sponsored by Google.
A veterans group that is backing Hagel's nomination also lamented the delay.
"Our enemies look for any moment — however brief — of weakness," said Jon Soltz, a Iraq War veteran and chairman of VoteVets.org.
Republicans, led by Sens. Lindsey Graham of South Carolina and John McCain of Arizona, insisted the White House tell them more about how Obama handled the Benghazi crisis.
Seeking to break the logjam, the White House responded to a Feb. 12 letter from Graham, McCain and Sen. Kelly Ayotte, R-N.H., to Obama asking whether he spoke to any Libyan government official during the Sept. 11 assault about getting assistance. Republicans have sought to portray Obama as being out of touch during the attack.
Clinton called Libyan President Mohamed Magariaf on Obama's behalf on Sept. 11 to coordinate additional support to protect Americans in Libya, White House counsel Kathryn Ruemmler wrote in the Feb. 14 response. Obama spoke to Magariaf on the evening of Sept. 12, she said.
Associated Press writers Richard Lardner, Jim Kuhnhenn, Donna Cassata, Laurie Kellman and Darlene Superville contributed to this report.