The Brazilian attacking-midfielder scored the only goal for his side in the shock 2-1 defeat at Levante in the first leg of their Copa del Rey last-16 tie on Thursday. However, despite scoring a crucial penalty late in the match, his overall performance was far from satisfactory, leaving his boss wanting more.
After the game, Valverde addressed the Coutinho conundrum, revealing what the player must do to play more regularly.
"When I wasn't playing Dembele everyone asked about him," Valverde said after the game, as quoted by Marca.
"Now he plays and Coutinho doesn't and it is the other way around.
Jeison Murillo made a forgettable debut for Barcelona, but Valverde said he was happy with his display.
"I'm happy with Murillo," the coach said.
"He showed his experience.
Barcelona youngster Juan Miranda suffered against Levante before being eventually replaced by Sergi Roberto.
"Miranda doesn't have any physical problems," he added.
"I had to change because it was the best thing I could do and I had to help the team.