In an e-mailed statement Thursday afternoon, Mr. Lehrer said he thought the new format accomplished its purpose, “which was to facilitate direct, extended exchanges between the candidates about issues of substance.” He continued, “Part of my moderator mission was to stay out of the way of the flow, and I had no problems with doing so. My only real personal frustration was discovering that 90 minutes was not enough time in that more open format to cover every issue that deserved attention.”

The critiques came from several sides of the media spectrum.

“Boy, Jim Lehrer got rolled over,” MSNBC’s Joe Scarborough said on “Morning Joe” on Thursday morning. “You could see an exasperated look on Jim’s face when they would just keep plowing right over him,” said Gretchen Carlson on “Fox & Friends” on Fox News. Speaking on CNBC Thursday morning, Steve Liesman offered up what he called a “private-sector solution” to the moderator dilemma: “Why can’t the two guys take care of themselves?”

The complaints about Mr. Lehrer seemed loudest from the left. Bill Press, whose liberal radio program is simulcast on Current TV, started on Thursday by saying Mr. Lehrer “lost control of the debate, and Mitt Romney ran all over him like a truck crushing a bug.” The liberal media monitoring group Media Matters said Mr. Lehrer had “lost the debate” by missing “repeated opportunities to press Mitt Romney into offering specifics on his policy proposals.” Richard Kim, a writer for The Nation, concluded that Mr. Lehrer’s version of moderation “is fundamentally unequipped to deal with the era of post-truth, asymmetric polarization politics — and it should be retired.”

The six-topic format for a debate primarily about domestic policy also drew complaints that many issues — gun control, abortion, reproductive rights, gay rights, the environment — were not addressed.

Alan Schroeder, a Northeastern University professor who has written books about debates, said that “in Jim Lehrer’s defense, this was an untested format.”

Mr. Schroeder said Wednesday’s session reminded him of televised debates he has studied in France and Spain, where “the role of the moderator is to set up the topics, then hang back and let the candidates go at it.”

The next debate between Mr. Obama and Mr. Romney will be moderated by Candy Crowley of CNN, who notably did not join the chorus of complainers about Mr. Lehrer’s performance on Wednesday night. She credited Mr. Lehrer for trying throughout his moderating career to get candidates to engage with each other.

“In the end, this debate is, you know, brought to you by these candidates,” she said on CNN after the debate, “and to me, it’s better to hear from the candidates than to hear from the moderator.”