The Brazilian was the star of the show in the win over Arsenal last week.
The Brazilian was the star of the show on the opening weekend, scoring two goals in the 4-3 win over Arsenal at the Emirates.
One of those was a sumptuous free-kick that is arguably a goal of the season contender already.
The display continued Coutinho’s impressive development under Klopp’s leadership, with him having vastly improved since the German arrived last October.
Liverpool's Philippe Coutinho celebrates scoring their third goal
And Carragher has admitted that the player’s improvement has come as something as a surprise to him.
“He [Coutinho] has surprised even me with the way he has responded to working with Jurgen Klopp,” he told the Daily Mail.
“I thought he would find the extra intensity difficult at first, especially playing in a wide role where you are required to cover more ground. He has actually gone up a level but there is still another level for him to reach.”
Liverpool's Philippe Coutinho celebrates scoring their first goal with teammates
It now remains to be seen if Coutinho can build on that strong first performance and enjoy a fine season with Liverpool this year.
He has often put in impressive displays like the one against the Gunners but has struggled to do that on a consistent basis during his time at Anfield.
Should he be able to rectify that, there is no denying that he could be set to reach that next level that Carragher wants to see him aim for.
Liverpool's Philippe Coutinho celebrates scoring their third goal with Nathaniel Clyne