Chargers general manager Tom Telesco also got the axe as the team fell to 5-9 with a fifth loss in six games.
The Raiders seized a 42-0 lead and threatened the NFL all-time scoring record in a regular-season game, the 72 points by Washington in a 1966 victory over the New York Giants.
"These decisions are never easy, nor are they something I take lightly -- especially when you consider the number of people they impact," Spanos said in a statement.
"We're clearly not where we expect to be, however, and we need new vision. Doing nothing in the name of continuity was not a risk I was willing to take."
The Chargers are set to miss the playoffs for the eighth time in 10 seasons. They have not gone beyond the second round of the post-season since the 2007 campaign.
"Our fans have stood strong through so many ups and downs and close games. They deserve more. Frankly, they've earned more," Spanos said.
"Building and maintaining a championship-caliber program remains our ultimate goal. And reimagining how we achieve that goal begins today."
The team said an interim head coach and general manager will be named soon. The Chargers do not play again until hosting Buffalo on December 23.
Staley, 41, was hired by the Chargers in January 2021 and went 24-24 with the club after stints as an assistant coach with Denver, Chicago and the Los Angeles Rams.
