"No one has been held responsible," he told moderator Bob Schieffer. "Apparently it may be, unfortunately, the old Washington game - not invented with this administration: 'We're all responsible, so no one is responsible.'
"The American people expect us to hold people accountable. And I intend as a member of the Homeland Security Committee, to see if we can't continue to find out who was responsible and hold them accountable," he said.
Earlier today an audio tape purportedly from al Qaeda leader Osama bin Laden was released, in which .
"I think that the events of last week and the way it was handled proved that there were significant errors made both in anticipating the Christmas bomber and putting together all the information that was obviously there," McCain said.
McCain said the tape indicates bin Laden is still "a motivating force for jihadists, Islamist extremists throughout the world.
"And so we have to stay after him," he said.
The senator complained that when Abdulmutallab was taken into custody following his failed attempt to detonate a bomb on board a Northwest Airlines jet, he received his Miranda rights.
"Any chance of finding out Osama bin Laden's connection with this bombing vanished when the decision was made - without consulting any of our intelligence heads - by apparently the Justice Department with directions to low-level of the FBI, to give this individual . . . a trial in civil court, which then gave him his Miranda rights, and he was lawyered up.
"He was cooperating until he got a lawyer," McCain said. "That, to me, is unbelievable."
Host Bob Schieffer asked him if "heads should roll" over the incident.
"There was a failure. And as soon as we find out the depth of those failures, obviously I think there should be changes made," he said.