The Catalan giants appear to have now ended their pursuit after failing to persuade the Reds to sell for £118million.
Coutinho put in a transfer request to try and force through a transfer.
But Liverpool owners Fenway Sports Group stood firm, having struggled to land Jurgen Klopp’s top targets this summer.
Mohamed Salah eventually arrived from Roma, but RB Leipzig midfielder Naby Keita and Southampton centre-half Virgil van Dijk have eluded the Reds.
Carragher believes the Coutinho saga is now over as Liverpool could not face selling.
But a departure would have been possible if Van Dijk and Keita had been acquired.
"They will hang onto Coutinho now, of course,” Carragher said on Sky Sports’ Monday Night Football.
“I don't think there is any doubt now.
“I said a few weeks ago that they can't sell him, but the problem is it becomes more political rather than the business of it.
"Liverpool have had such a poor window, they couldn't be seen to be letting go of him.”
On incomings at Anfield, Carragher added: “Now if Liverpool three big targets of Virgil Van Dijk, Naby Keita and Mo Salah had all come in the door, it may have been easier to prise [Coutinho] away.
"Even a supporter might have thought '120m for Coutinho?' with the ability to go and spend that with a few weeks of the season to go.
“But they were never going to sell him because of the fact they had not bought enough players in."
Liverpool are still hunting Van Dijk, but they are likely to have to wait until next summer to potentially land Keita.
