Tsarnaev and his brother were only identified three days later when authorities released photos and video footage of them at the scene of the blasts.
"I just find it really unnerving that we could have had him in FBI custody in 2011 and did a whole profile of him, and after the attack that his name not surface, that we didn't check the database or the database had him missing," Graham said.
Tsarnaev was an immigrant from the volatile Caucasus region of southwest Russia who had legal residence in the United States and sought last year to become fully naturalized, like his brother Dzhokhar, 19.
However, the Department of Homeland Security rejected the citizenship request due to the FBI questioning before the Russia trip.
An FBI statement Friday said a foreign government -- later identified by legislators as Russia -- asked for information on Tsarnaev "based on information that he was a follower of radical Islam and a strong believer, and that he had changed drastically since 2010 as he prepared to leave the United States for travel to the country's region to join unspecified underground groups."
In response, the FBI said, it "checked U.S. government databases and other information to look for such things as derogatory telephone communications, possible use of online sites associated with the promotion of radical activity, associations with other persons of interest, travel history and plans, and education history."
"The FBI also interviewed Tamerlan Tsarnaev and family members," said the FBI statement. "The FBI did not find any terrorism activity, domestic or foreign, and those results were provided to the foreign government in the summer of 2011."
In addition, the FBI "requested but did not receive more specific or additional information from the foreign government," its statement said.
The lengthy travel to Russia by Tsarnaev, who's ethnically Chechen but came to the United States from Kyrgyzstan, caused some legislators and analysts to speculate he may have received training during the trip.
Fuentes detailed how the FBI employs what amounts to "triage" to deal with what he said were tens of thousands of similar inquiries a year that require some level of bureau investigation.
"If you are getting this from a hot place like Afghanistan or the tribal area of Pakistan or places where we have had specific training camps and people deployed on purpose to come and attack us, then that is the highest priority," he said. "And even there, many of the people that go back and forth are visiting family. I mean, they are not always going back to be trained to be terrorists or always going back for refresher courses on terrorism."
Regarding Russia, Fuentes noted the ongoing conflict with Chechen separatists that may have caused Moscow's request for information on Tsarnaev.
"That's been an ongoing fight, but it's been localized," he said, adding that he couldn't recall a case in which a Chechen trained at home came to attack the United States.
However, Fuentes noted that al Qaeda had sent people to the Caucasus region for training that included bomb building.
Now U.S. investigators need to find out if the Tsarnaevs "had connections, were they deployed by a bigger group, and are there other terrorists in the United States," Fuentes said.
"Are there other explosive devices hidden somewhere or booby traps created, a cache of weapons?" he wondered. "That'll be the task."