Mohamed Salah headlined Liverpool's arrivals this summer but the Merseyside club were also heavily linked with moves for Virgil van Dijk and Naby Keita, which ultimately did not pan out.
With the news that Coutinho handed in a transfer request recently, having been linked with a move to Spain, Liverpool are still holding firm and have rejected a third bid from Barcelona, believed to be worth £118m ($151.9m) inclusive of add-ons.
While it remains to be seen whether a fourth bid will arrive, Carragher believes the Brazilian will remain at Anfield while admitting that a transfer was possible if Liverpool managed to land their desired trio.
"Well they will now of course," Carragher said when asked if Liverpool will keep Coutinho, as quoted on The Express. "I don't think there's any doubt now. I said it a few weeks ago that they can't sell him."
"The problem is it becomes more political than the actual business side of things. Liverpool have had such a poor window they couldn't be seen to let him go.
"Liverpool's three big targets of Van Dijk, Keita and Salah. If they'd got them in the door, I'm not saying yes to selling Coutinho but it may have been easier to prise him away.
"Even Liverpool supporters may have thought '£120million for Philippe Coutinho? We can still go and spend that in two or three weeks to go'. But they were never going to sell him on the fact that they haven't brought enough players in."
Coutinho is yet to appear for Liverpool since making his last appearance for the Reds in pre-season on 1 August.
The 25-year-old has also missed all three of the club's games this season as he recovers from a back injury.