"The result is that the public remains in the dark about how exactly U.S. policy governing targeted killings is operating, under which legal authorities, and who exactly are its victims," said a letter to Obama in December from nine rights groups.
Hina Shamsi, who directs the ACLU's National Security Project, told CNN that the Obama administration was "fighting hard" to prevent a judicial review of the strikes that killed al-Awlaki and the other Americans, including the terrorist's 16-year-old son.
Until allegations in classified documents can be assessed in court, she said, the question of whether they amount to real evidence remains unanswered.
Shamsi called the U.S. actions "one of the most extreme and dangerous forms of authority that the executive branch can claim -- the power to kill people based on vague and shifting legal standards, secret evidence and no judicial review even after the fact."
In 2010, a federal judge in Washington noted the government would need permission from a federal court to wiretap al-Awlaki, but that no such court process existed in order to kill him.
Rejecting an effort by al-Awlaki's father to block his son's possible extrajudicial killing, U.S. District Judge John Bates called it "somewhat unsettling" that a president could -- for national security reasons -- make a unilateral decision to kill a U.S. citizen overseas and the decision would be "judicially unreviewable."
Critics: Obama's anti-terrorism strategy confusing
Obama has insisted his responsibility as commander in chief to protect Americans from attack justified targeted killings such as the drone strike on al-Awlaki.
In a May speech, he rejected targeting an American citizen without what he called due process, meaning adherence to full legal procedures. Then he explained the reasoning for the 2011 hit on al-Awlaki before the expanded policy guidelines he was announcing.
"When a U.S. citizen goes abroad to wage war against America and is actively plotting to kill U.S. citizens, and when neither the United States nor our partners are in a position to capture him before he carries out a plot, his citizenship should no more serve as a shield than a sniper shooting down on an innocent crowd should be protected from a SWAT team," Obama said.
"I would have detained and prosecuted Awlaki if we captured him before he carried out a plot, but we couldn't," Obama continued. "And as president, I would have been derelict in my duty had I not authorized the strike that took him out."
Critics, including congressional Republicans, argue the president's anti-terrorism strategy, which in many ways extended programs and practices started under the Bush administration, have failed to curtail al-Qaida.
Asked last week at a congressional hearing if al-Qaida was stronger or weaker than before the 9/11 attacks, Director of National Intelligence James Clapper conceded the terrorist network was more widespread.
At the same hearing, House Intelligence Committee Chairman Mike Rogers argued that tighter restrictions on targeted killings announced last year had weakened the government's fight against terrorism.
"Today, individuals who would have been previously removed from the battlefield by U.S. counterterrorism operations for attacking or plotting to attack against U.S. interests remain free because of self-imposed red tape," the Michigan Republican said, adding that Obama's "May 2013 policy changes for the U.S. targeted strikes are an utter and complete failure, and they leave Americans' lives at risk."
Rogers complained the problem involved confusion over U.S. policies.
The ACLU's Shamsi accused the administration of failing to adhere to the policies of increased oversight and observance of due process.