"Like every decision, it comes down to what's best for the team and what gives us the best chance to win," coach Ken Whisenhunt said in a statement released by the team.
Pendergast's departure leaves the team without both coordinators. Offensive coordinator Todd Haley was named head coach of the Kansas City Chiefs on Friday.
Pendergast was hired by Dennis Green in 2004 and stayed on when Whisenhunt took over in 2007.
"He was one of the guys retained from the previous staff and has done a good job," Whisenhunt said. "But as part of the evaluation process that's done after every season, I took a look at the last two years as a whole and felt this move was necessary to help us continue the progress we've made."
"From a timing standpoint, we wanted to be fair to Clancy and give him a chance to seek the best possible opportunity in which to continue his career," Whisenhunt said. "In terms of filling the position, we have some people in mind both internally and externally and will begin that process immediately."
The Cardinals ranked 19th in the NFL in overall defense in the regular season, giving up 331.5 yards per game. They were 22nd in pass defense and 16th against the run.
Pendergast was known for using a variety of blitz and coverage schemes aimed at taking advantage of the Cardinals' speed.
The defense struggled in blowout losses to Philadelphia, Minnesota and New England late in the regular season, but stepped up in the playoffs, shutting down the powerful running games of Atlanta, Carolina and Philadelphia in the run to the Super Bowl.
Against the Steelers, the defense played well until the last-minute drive that ended with the touchdown pass from Ben Roethlisberger to Santonio Holmes with 35 seconds to play that gave Pittsburgh a 27-23 victory.
Pendergast graduated from the University of Arizona in 1990, then was a graduate assistant for Mississippi State before working on the staffs at USC, Oklahoma and Alabama-Birmingham.