Neymar had already seen a penalty overturned by a VAR review before scoring the second of Brazil's second-half injury-time goals after Coutinho broke the deadlock.
Following the game, the superstar forward was seen in tears with his head in his hands as his team-mates celebrated a crucial Group E victory in St Petersburg.
And Barca midfielder Coutinho believes Neymar's attitude to the game helps drive Brazil on.
"Neymar had a difficult injury and went through a very bad patch," he said in a post-match news conference.
"His joy of being back on the pitch is contagious. Everyone is really happy that he is back on the pitch and scoring."
Brazil struggled to break down Costa Rica, but Coutinho says their late show is a sign of the strong mentality in the squad.
"It was a tough game, as we expected. We were aiming for victory from the first minute and we had the patience to play to the end of the game when we were rewarded with two goals," he added.
"The responsibility is huge when you are playing for the national team. You have to be mentally strong from the beginning to the end.
"If you score in the first minute or the last you still have the 90 minutes to fight and that is what happened – we fought to the end.
"The most important thing in our team was not giving up until the last minute."