"Gerard Houllier had the same thing thrown at him when Patrice Bergues left, and in that case I do think that had a big impact," Carragher told liverpoolfc.tv.
"I got on great with Pako, he was superb at his job and he had a great relationship with the manager, but he was the fitness coach.
"Rafa is the coach. At the end of the day, we've lost a fitness coach, not a football coach, although it's a fitness coach who was outstanding at his job.
"But it's still the manager picking the team. Rafa is the football man and that hasn't changed, and I'm sure the results since Pako has left is just a coincidence.
"I can understand why people might look at that. People are always looking for reasons why a team isn't playing so well, but in the training sessions we are still doing the same things.
"If people do look at Pako leaving as the reason for our loss in form, I think they are looking for excuses really."