The Obama administration Tuesday praised law enforcement officials who discovered and dismantled the bomb in New York City last weekend, and who arrested a suspect late Monday. But the fact remained that Faisal Shahzad was allegedly able to train with terrorists in Pakistan, return to the United States to assemble a car bomb in Connecticut and park it in Times Square without anyone in the nation’s vast counterterrorism apparatus knowing anything about it.

Senior administration officials cited two instances in which the system could have worked more effectively. On Monday night, sometime between the FBI’s discovery of Shahzad’s identity and whereabouts and his removal from an Emirates airline plane that was about to depart from John F. Kennedy International Airport, agents “lost him,” one official said.

“It does beg the question why he wasn’t apprehended before arriving at the airport or boarding the plane,” one official said.

Officials also pointed to Emirates’ failure to update its no-fly list in response to federal bulletins Monday afternoon, allowing Shahzad, who arrived at the airport at 7:35 p.m. after booking his flight from his car on the way, to board the 11 p.m. flight.

Another senior official acknowledged that the system is not foolproof but insisted that it has improved. “We have a system that is built with redundancy and that is agile, increasingly so,” he said. “So while it’s our job to worry — and to act on those worries — we also feel like we have a system that’s been improved over time.”

New York Police Commissioner Raymond Kelly, who appeared at a news conference Tuesday with Attorney General Eric Holder and Homeland Security Secretary Janet Napolitano, described federal and local cooperation as “seamless.”

But some Republicans noted that the attempt was not prevented, and they criticized the administration for its actions after the bomb was discovered, including reading Miranda rights to Shahzad just hours after his arrest. Officials said he was initially questioned without those rights, under a “public safety” exemption, and was read those rights — he waived them — as he continued to cooperate with law enforcement.

Lawmakers on both sides of the aisle suggested that there is a basic hole in the intelligence system that is difficult to fill. “Increasingly, the dilemma is the well-educated man who moves through the education system of our country somewhat promisingly,” said Sen. Richard Lugar, R-Ind.; Shahzad is a graduate of U.S. universities.