Fallout from the attack and the investigation's conclusion forced four State Department officials to step down on Wednesday.
"We learned some very hard and painful lessons in Benghazi," Burns told the Senate Foreign Relations Committee. "We are already acting on them. We have to do better."
At a relatively low-key hearing, Republicans tangled with the officials over whether warning signs of a deteriorating security situation were ignored and why the department didn't ask Congress for money to boost security at the diplomatic mission in Benghazi.
U.S. Ambassador Chris Stevens and three other Americans were killed in the attack.
"We made the mistaken assumption that we wouldn't become a major target," Burns told the panel.
Sen. Jim Inhofe, R-Okla., ticked off a long list of incidents involving Westerners in the months before the Libya raid, including attacks with rocket-propelled grenades and improvised explosive devices. Just two days before the assault, Stevens had requested additional security.
Burns pointed out that report found no "specific tactical threat," but conceded to Inhofe that he was correct to identify a troubling pattern.
"We did not do a good enough job in trying to connect the dots," Burns said.
The hearing provided an odd scene as the panel's chairman, Sen. John Kerry, D-Mass., is a top candidate to replace Clinton as secretary. Kerry presided at the hearing, but asked no questions of officials who could be his future employees.
In an opening statement, Kerry said the department had "clear warning signs" of a deteriorating security situation in Libya prior to the attack. He also faulted Congress for failing to provide sufficient funds to protect facilities worldwide.
Kerry complained that lawmakers have provided far less money to the State Department, forcing it to scramble to cover the costs of securing diplomatic installations. The department is seeking $1.4 billion in next year's budget for increased security, money that primarily would come for funds that haven't been spent in Iraq.
The money would cover $553 million for 35 additional Marine Security Guard detachments, $130 million for 155 diplomatic security personnel and $376 million for security upgrades and construction at new embassy compounds.
Joining Burns was Deputy Secretary of State Thomas Nides, who is in charge of management, at back-to-back congressional hearings.
Stevens was killed in the attack along with information specialist Sean Smith and former Navy SEALs Glen Doherty and Tyrone Woods, who were contractors working for the CIA. Stevens was the first U.S. ambassador killed in the line of duty since 1979.
An unclassified version of the report by the Accountability Review Board concluded, "Systematic failures and leadership and management deficiencies at senior levels within two bureaus of the State Department resulted in a Special Mission security posture that was inadequate for Benghazi and grossly inadequate to deal with the attack that took place."
The report singled out the Bureau of Diplomatic Security and the Bureau of Near East Affairs for criticism, saying there appeared to be a lack of cooperation and confusion over protection at the mission in Benghazi, a city in eastern Libya that was relatively lawless after the revolution that toppled Libyan strongman Moammar Gadhafi.
Obama administration officials said those who resigned were Eric Boswell, assistant secretary of state for diplomatic security; Charlene Lamb, deputy assistant secretary responsible for embassy security; and Raymond Maxwell, deputy assistant secretary of state who oversees the Maghreb nations of Libya, Algeria, Tunisia and Morocco. The officials spoke on condition of anonymity because they weren't authorized to discuss personnel matters publicly.
Some of the three may have the option of being reassigned to other duties, said the officials.
State Department spokeswoman Victoria Nuland said the department had accepted the resignations of four people: Boswell and three others she declined to identify.
The resignations did little to mollify lawmakers who insisted that Clinton testify in the coming weeks despite her plan to leave the administration. Kerry said she would appear before the panel in January.
Clinton had been scheduled to testify before the committees but canceled after fainting and sustaining a concussion last week while recovering from a stomach virus. Clinton is under doctors' orders to rest.
"She is ultimately responsible for the department and U.S. posts around the world. Her testimony before the Senate Foreign Relations Committee is indispensable to any effort to address this failure and put in place a process to ensure this never happens again," Sen. Marco Rubio, R-Fla., said.
The report's findings underscore a fundamental problem the State Department has been trying to address for decades without success: how to protect diplomats while allowing them to perform their duties to reach out to foreign governments and the public to promote U.S. interests and values.
In a letter to Congress, Clinton said "our diplomats cannot work in bunkers and do their jobs."
"When America is absent, especially from dangerous places, there are consequences," she said. "Extremism takes root, our interests suffer, and our security at home is threatened. We must accept a level of risk to protect this country we love and to advance our interests and values around the world."
The American Foreign Service Association, the union that represents U.S. diplomats, said it agreed. It welcomed the findings and accepted the board's 29 recommendations for improving embassy security, particularly at high-threat posts.
"There is inherent risk in the practice of active and effective diplomacy, and our diplomatic personnel will always be exposed to a degree of harm in the line of duty," the association said in a statement. "It is our responsibility to do all we can to minimize the risk and balance it with the importance of the mission and to ensure that the missions we undertake have the personnel and financial resources to achieve policy goals."