Second, Murphy will make the choice of the next head coach, with input from general manager Brian Gutekunst.
Regarding the decision to fire McCarthy, who will be replaced on an interim basis by Joe Philbin, Murphy said, "I think we all would have preferred to do this after the season, but the performance on Sunday made it clear a coaching change was necessary."
He called the 20-17 loss to Arizona "unacceptable."
When asked whether McCarthy would have been fired if Packers kicker Mason Crosby had made a 49-yard field goal on the final play to send the game into overtime, Murphy hedged, saying he did not want to answer a hypothetical question. But he again noted that Sunday's game was the final straw.
"Up until yesterday, we were hopeful we'd get a big win and kind of turn the season around," he said. "The performance Sunday really sealed it for me. We did not play well. To lose to a 2-9 team at home to an Arizona team, from a dome. It was not a good performance."
The loss dropped Green Bay's record to 4-7-1 and it has lost three straight.
Murphy noted the part quarterback Aaron Rodgers played in the decision.
"Aaron was not part at all in the decision to move on from Mike," he said.
Both Murphy and Gutekunst said they would accept Rodgers' input on the hiring of the next coach but that he would not be part of the selection process.
As far as making the coaching change now, instead of after the season, Murphy said, among other things, "It gets us into the market earlier, and the side benefit is for Mike."
Indeed, McCarthy could be a candidate for other coaching jobs that become available.
Murphy noted that Philbin would be considered for the head coaching job on a permanent basis, depending on how things go in the final four games.
When asked who will make the choice of a new head coach, Murphy said, "I will. Brian will be actively involved. I'm not going to hire a coach that Brian is not comfortable with."
Philbin, who is in his first year of his second stint as the Packers' offensive coordinator, said he will continue to call the offensive plays. He said the focus is entirely on the next game against the Atlanta Falcons.
He said he hasn't slept much since the decision was made, and was not happy with the offense's production, which is his responsibility, and how that might have impacted McCarthy's job status.
"You feel like you let him down," Philbin said.
Philbin had previously been the head coach of the Miami Dolphins before being fired after the 2015 season.
He knows he has a lot of time-consuming responsibilities in the coming days.
He also noted that Monday was his 30th wedding anniversary.
"She's expecting a big dinner," he said, then paused, and said softly, "don't hold your breath."
Kicker Mason Crosby missed a potentially game-tying 49-yard field goal Sunday afternoon. It marked his seventh missed field goal and ninth missed kick overall on the season. His field goal percentage dropped to 75.9 percent.
Wide receiver Jake Kumerow made his first career catch, an 11-yard reception on the Arizona sideline on second-and-10 that helped set up the Packers' game-tying touchdown in the fourth quarter.
Quarterback Aaron Rodgers attempted 50 passes on Sunday (completing 31). It is the second time this season Rodgers attempted 50 passes or more. Green Bay lost both.
Running back Aaron Jones was the Packers' leading rusher on Sunday with just 36 yards on 11 carries. It was his lowest rushing total of the season.
Wide receiver Davante Adams had eight receptions for 93 yards on Sunday, giving him 85 catches for 1,115 receiving yards for the season.