During the summer, Benitez bemoaned the resources available to him after Newcastle failed to secure their main targets, even though the club owner Mike Ashley had promised to give the former Liverpool and Real Madrid manager "every last penny" to bolster his squad.
Some of Benitez's predecessors at St James' Park have found it difficult to deal with the Sports Direct tycoon and Carragher expects Benitez will follow suit sooner rather than later.
"If I'm being totally honest, I don't expect to see Rafa Benitez at Newcastle over a sustained, long period of time," Carragher said on Sky Sports' Monday Night Football.
"I think eventually something will happen with him and the owner and unfortunately for Newcastle this is not going to be a happy and long marriage. So enjoy it while he's here."
Newcastle's 1-0 defeat at Brighton on Sunday (24 September) was their first after three consecutive wins and the Magpies sit comfortably in mid-table, a situation few envisaged after two consecutive defeats in the opening two games.
Carragher, who played for six years under Benitez during the latter's spell at Liverpool, suggested the recent run of result proved Newcastle were unlikely to find themselves drawn into a relegation battle in the latter stages of the campaign.
"I don't think there's any chance of Newcastle going down, just because of the manager. He is very pragmatic and he'll make it very difficult," he said.
"In every game Newcastle have, you'll very rarely see them lose 4-0 or 5-0, as you might see teams in the bottom half of the table. I think that's where Newcastle will be, but I don't expect to see them in a relegation fight."
Newcastle host Liverpool on Sunday and Carragher expects Benitez to make life hard for his former side, who have won just once in their last six visits to St James' Park in the Premier League.
"I don't think Liverpool have got an easy game going to St James' at the weekend," said the former Liverpool defender.
"You saw how they were against Tottenham Hotspur [in their first game of the season] before they went down to 10 men."