Commander Amir Ali Hajizadeh revealed an operator made the decision to fire at the aircraft in 10 seconds.
At least six people have so far been killed in the unrest, which erupted last week over increases in the price of gasoline.
Wednesday's drone shoot down is the latest in a series of escalations that threaten to push Washington and Tehran into open conflict.
"The United States is a regime formed on the basis of capitalism, racial discrimination and hegemonism," Major General Mohammad Ali Jafari said.
Iranian military spokesman Abolfazl Shekarchi has said the attack was carried out by groups linked to the U.S. and Israeli intelligence.
Revolutionary Guards Naval Commander Rear Admiral Ali Fadavi claimed his military speedboats could cruise circles around U.S. warships.
Iranian Major General Qassem Soleimani, commander of the Islamic Revolutionary Guard Corps' Quds Force, has left the shadows for the spotlight.
At least 21 people have been killed in the protests, the largest in Iran since 2009.
Iran has rallied groups across the Middle East against what it perceives to be the combined interests of ISIS, Israel, Saudi Arabia and the U.S.
Iran is looking to project its military power and establish ties abroad at a time when the U.S., Israel and Saudi Arabia have tried to isolate it.
Ayatollah Ali Khamenei said President Donald Trump has insulted the Iranian people ahead of an important national holiday.
Brigadier General Hossein Salami said Trump could not back up his threats with military force.
The Pentagon is conducting a major review as Iran announces the U.S. military has been added to a list of groups threatening regional stability.
Iran has threatened a "crushing" response to the U.S. potentially designating its elite Islamic Revolutionary Guard Corps as terrorists.
The USS Thunderbolt reportedly fired at an Iranian ship that came within 150 yards and may belong to the elite Iranian Revolutionary Guards Corps.
Tehran claims the Saudi Arabian border guards opened fire on Iranian fishermen.
Some of the 10 crew members gave away capabilities of their vessels, one of them disclosing his vessel's potential speed and suggesting it was on a "presence" mission to demonstrate U.S. military power in the Gulf.
Iran is expecting an economic boom in the post-sanctions era.
Iran's Revolutionary Guard Corps has many ways to wage a long cold war between Tehran and its Arab foes.