The Liverpool legend could not resist poking fun at the Manchester United great and TV sparring partner, after deciding to part ways with their coach on Tuesday.
Salford - the League Two club co-owned by Neville - are now searching for their fourth manager in just two years following Bowyer's departure.
The 50-year-old was given the chop after failing to guide the ambitious side to the League Two play-offs, with the Ammies finishing tenth in the table.
Bowyer signed a two-year contract last May, but is now the latest managerial casualty at Moor Lane.
And Sky Sports pundit Carragher didn't pass the opportunity to ridicule his fellow TV host, Neville, on social media after the news broke.
The former defender posted on Twitter: "Gary Neville puts more people out of work than Boris Johnson."
It's likely that hit a nerve with Neville - a vocal critic of the Prime Minister - but Carragher's jibe failed to prompt a reaction.
A statement on the club's official website, read: "Salford City Football Club announces the departure of first team manager Gary Bowyer from the Peninsula Stadium.
"A meeting was held earlier today and the club has made the decision to terminate Gary Bowyer's contract along with assistant manager Billy Barr.
"The club would like to thank Gary and Billy for their hard work over the last season, and we wish them all the best for their future roles within football.
"An announcement regarding the role of first team manager will be made in due course."
Bowyer becomes the third boss to have been sacked by Neville at Salford in two years, following Graham Alexander and Richie Wellens out the door.
Alexander was sacked in October 2020, despite helping the club secure promotion to League Two.
After his dismissal, Neville later admitted he made a mistake and regretted his decision.
"Last season, Graham Alexander should never have left this club," he said. "He should never have left, I should never have made that decision that I made.
"It goes against everything that I believe in and that's what owning a football club does to you, it takes you to that place where you do things that you don't believe you ever would do."