Coutinho scored Barcelona's only goal in the 2-1 Copa del Rey defeat away to Levante but delivered an overall poor performance.
Valverde has called for the Brazilian to work as hard as he can to get himself back in the starting XI and to put pressure on those who are playing more often.
"When I wasn't playing Dembele everyone asked about him," Valverde said after the game.
"Now he plays and Coutinho doesn't and it is the other way around.
"The players have to work to turn things around.
"He is not happy, he has to fight, but one or the other almost always plays and Coutinho gives us a lot and will give us a lot."