McCarthy was sacked at the weekend after 13 years with the Packers, helping the side win the Super Bowl in 2010.
McCarthy has been replaced by Joe Philbin on an interim basis, with Philbin most recently a head coach for the Miami Dolphins from 2012-2015.
Rodgers had been a mainstay under McCarthy, the quarterback considered as one of the greatest of all time in the NFL.
But despite bringing plenty of success to Green Bay, Rodgers has admitted he and McCarthy didn’t always see eye to eye.
“Like any relationship we’ve had amazing times and times when we butt heads,” Rodgers said.
“We accomplished a lot together.
“Like I said, it’s tough. You spend that much time together, so many years, and you have a close working relationship and a close friendship off the field.
“It’s tough. I’m sure he’s going through the grieving process, as many of us have known him for a long time and worked with him are as well.
“I think we were all surprised last night. There was a great deal of frustration about the performance [against Arizona], individually and collectively as a squad losing a game we should have won, and surprised about the timing.
“But those are decisions [team president] Mark [Murphy] is making with [general manager] Brian [Gutekunst’s] help and we’re going to keep moving forward.”
Philbin has worked alongside McCarthy as offensive coordinator from the start of this season.
Packers president and CEO Mark Murphy explained in a statement that the poor results this year led to the decision to fire McCarthy.
“The 2018 season has not lived up to the expectations and standards of the Green Bay Packers,” he said.
“As a result, I made the difficult decision to remove Mike McCarthy of his role as head coach, effective immediately.
“Mike has been a terrific head coach and leader of the Packers for 13 seasons, during which time we experienced a great deal of success on and off the field.
“We want to thank Mike, his wife, Jessica, and the rest of the McCarthy family for all that they have done for the Packers and the Green Bay and Wisconsin communities.
“We will immediately begin the process of selecting the next head coach of the Green Bay Packers.”