The former Liverpool defender also believes that Brendan Rodgers's side will need the Brazilian on top form to beat Arsenal.
The Brazilian has become Liverpool’s star performer in recent seasons, with a number of wonder goals having put the pressure firmly on his shoulders.
Coutinho has already managed one wonder goal this season to help his side beat Stoke City in their opening game of the 2015-16 Premier League campaign.
However, most of his top performances have come at Anfield, and Carragher says the next step is for him to start performing away from home against the big teams.
“Probably the next step for Philippe Coutinho is to put in a few performances especially away from home against the really big teams,” he wrote on Skysports.com.
“I think he's good at home especially the last couple of years against Man City [and] he scored against Arsenal at home last season as well, but I think the next step for Coutinho is to start really producing in really big away games.”
Liverpool need Coutinho performing to beat Arsenal
After securing two wins from two games with a win over Bournemouth on Monday, Brendan Rodgers' side now face a visit to Emirates Stadium in arguably their first big test of the new season.
It will be a difficult challenge for the Reds as they were heavily beaten by Arsenal away from home last season, while Arsene Wenger’s side are sure to be keen to dispel any doubts on them after their opening game defeat to West Ham.
And Carragher believes that Coutinho must be on top of his game if his old side is to leave London with a positive result.
“He is brilliant and he has carried on from last season, he's Liverpool's best player at the moment,” he added.
“If you want to do well in the big games away from home you need your best players to perform so I think if Liverpool are going to get a result on Monday they really need Philippe Coutinho to perform.”