The attack on a house in North Waziristan tribal area near Afghanistan May 29 killed Taliban deputy leader Waliur Rehman.
The U.S. government had placed a $5 million bounty on Rehman, 42, who was believed behind many attacks on U.S forces in Afghanistan.
Sharif, whose Pakistan Muslim League-N won last month's parliamentary election, said in a statement released by the party that he had "serious concern and deep disappointment" at the strike.
The attack violated international law and the U.N. Charter, the statement said. It also came within days of U.S. President Barack Obama setting out a new policy on drone attacks designed to ensure closer cooperation between the countries.
Unilateral measures such as drone attacks aren't the way forward, Sharif's statement said.
U.S. Secretary of State John Kerry has defended the attack as self-defense and therefore legal because the United States is fighting a war with al-Qaida and the Taliban.
Kerry said drones have killed terrorist commanders, trainers, bomb makers and operatives.
Immediately after the attack, the Taliban said peace talks with the incoming government were "terminated," The Wall Street Journal reported.
"The government is killing our leadership in collusion with the U.S. And yet it speaks of peace talks," Tehrik-e-Taliban Pakistan spokesman Ehsanullah Ehsan said.
The militant group vowed to avenge the leader's death and charged the Pakistani government had approved the U.S. drone attack.
Rehman had been a top Pakistan Taliban member since 2005 and was a spokesman for the group's former leader Baitullah Mehsud, who was killed in a drone strike in 2009. The TTP is now led by Hakimullah Mehsud.
Sharif made his statement regarding the drones last week before being sworn in as a member of Parliament in the National Assembly on Saturday.
The swearing in marks the first transition of power between democratically elected governments in the 66-year history of Pakistan.
When Sharif is elected by Parliament to lead a coalition government this week he will take over 13 years after he was ousted in a military coup led by Gen. Pervez Musharraf who returned to Pakistan from self-imposed exile to run in the election.
But Musharraf's election plans came undone when he was put under house arrest because of outstanding charges relating to the death of former Prime Minister Benazir Bhutto.
Last month a Pakistani court granted bail to Musharraf accused of failing to provide adequate security for Bhutto before her assassination while campaigning in 2007.
Musharraf, 69, will appear in a Lahore court June 10 to contest the charges, a report by Asian News International said.
His government dismissed a 2010 U.N. report, which said the government failed to provide enough protection for Bhutto while she was campaigning in Rawalpindi.