"The attack was ineffective and there were no casualties or damage to property reported," Bedean said in a statement shortly after the strike.
The rocket strike comes weeks after four NATO troops were killed when a Taliban suicide bomber attacked a convoy of coalition troops on patrol in Khost province in eastern Afghanistan.
Twenty Afghan civilians were also killed in the Oct. 1 blast, according to recent reports.
The Bagram attack also came as Kerry and Afghan President Hamid Karzai agreed to a preliminary postwar deal that lays the groundwork for a possible U.S. troop presence in Afghanistan after the White House's 2014 withdrawal deadline.
"This is an enormous transition. It’s an historic moment for this country. And we are proud and pleased to be able to work at being part of it," Kerry said during a joint press conference with Karzai in Kabul on Sunday.
Once approved, Karzai noted the deal could bring a realistic end to the years of violence and bloodshed in Afghanistan.
"The security agreement between Afghanistan and the United States ... will provide us with the things that we did not have during the past 10 years in Afghanistan, which is the safety of the Afghan people as well as the national sovereignty," he said.
But immunity for American troops in postwar Afghanistan remains an open question, despite the preliminary plan announced by Washington and Kabul.
"We don’t have a common understanding on this, and such an issue is beyond Afghan government authority," Karzai told reporters.
For his part, Kerry pushed back against the idea that American forces in country after 2014 will be above U.S. or Afghan law.
"In our judgment, there is no immunity in this agreement. Anybody who were to do anything [illegal] will be subject to the law," Kerry told reporters in Kabul.
Lack of immunity for U.S. troops was a crucial factor in the failed attempt to set up a postwar security deal in Iraq, and it set the stage for the recent wave of sectarian violence against Iraqi forces and civilians in the country.
Kerry reiterated that lack of an immunity deal will have long-term ramifications to Afghan security in the years after U.S. forces leave the country.
"There are realities that if it isn’t resolved," Kerry said.
"We can’t send our forces in places because we don’t subject United States citizens to that kind of uncertainty with respect to their rights and lives ... so that is a very important principle," he added.
Karzai is set to meet with the Loya Jirga, an assembly of the country's most powerful tribal leaders, in the coming weeks to seek their approval of the postwar plan drafted over the weekend.