Carragher has accused Arteta of employing time-wasting tactics regularly.
"I’ve been thinking about this for a long time, probably going back to this fixture last year," Carragher said on Sky Sports.
"Because Mikel Arteta worked with Pep we all think he is a Pep Guardiola disciple. If you look at the two most successful managers in the last 10-15 years you’ve got Pep on one end and Jose – almost equally successful – at the other end.
"Mikel Arteta is slowly morphing into a Jose Mourinho type of manager and no one really thought that would happen. They were 2-1 up, pressing Liverpool, on top and playing really well but they retreated in the second half.
"I know they had a couple of injuries at the back but they still got the midfield players and some attackers who you think you can get on the ball and go forward and try and take the sting out of the pressure you’re under. But that instinct to protect comes from the manager but it happens too often.
"I get what happened at City – I thought what they did was brilliant – but what they did here at Brighton, what they did against Bournemouth – the top teams when they go down to ten men, yeah, you are under pressure but you relieve it; you keep the ball a bit more and you’re still a threat going forward.
"It feels like what Jose was like at the Nou Camp with Inter (in the 2010 Champions League). This is not a criticism, this is an observation.
"But this idea that Arsenal play great football and he is a Pep Guardiola man, he is not. Just look at the players going down today, the secrecy before the game about who was fit and who wasn’t. It’s all out of the Jose Mourinho playbook."