Herbert responded, via a written statement, that he has been a strong advocate and defender of Hill.
Herbert championed a 2012 state appropriation to help the Utah Defense Alliance fight for the base in a future round of base closures, his news release said.
The Ogden Air Logistics Center was formally closed in a ceremony last month and the Ogden Air Logistics Complex took its place.
The 309th Maintenance Wing was also deactivated, and the center's 8,000 employees now work for the Air Force Sustainment Center at Tinker Air Force Base in Oklahoma. Hill lost 159 jobs, including some managers who moved to Oklahoma.
Last November, when the Air Force announced there would be major restructuring in Air Force Materiel Command to save $109 million, Herbert and Utah's congressional delegation angrily complained that they were not consulted about the impact at Hill.
In the ensuing months, the delegation met with Air Force leaders, but failed to persuade them to reverse the reorganization at Hill.
Cooke blasted state leadership he didn't call out the governor by name for not doing more to learn the Air Force's rationale and protect the base from what he says is a demotion.
"Nobody in our state was aware of this huge realignment of leadership and responsibility," Cooke said. "You need to be on top of what the Air Force is doing in your own state."
The candidate said he would press Air Force generals to increase the mission at Hill if elected.
Herbert's news release included comments by Utah Republicans Sen. Orrin Hatch and Rep. Rob Bishop, who supported Herbert's efforts for the base.
The governor, Hatch said, has been "instrumental in the mission to keep Hill Air Force Base firmly cemented in our state."
Bishop said it is President Obama's "trillion dollar cuts to defense" that are forcing changes at military installations. He called Cooke's comments "unnecessary and unconstructive."