Coutinho was brought on for the final 20 minutes of the Catalan giants' 2-0 victory at Camp Nou on Thursday night, three weeks after joining from Liverpool in a £142m transfer.
The 25-year-old did not make any serious impact on the match, but he did show the odd glimmer of what is to come when linking up with superstar forward Lionel Messi in attack.
Speaking to reporters after the game, Valverde said: "We have a lot of hope for him. In the sense that he will be good for our game, he can help us with his self-confidence, his ability one-on-one, to see the free player when he is close to the area, the danger is sensed.
"[Coutinho had] a simple game, but I think it went well. Let's see, this is the beginning."
Barcelona prevailed 2-1 on aggregate against rivals Espanyol to book a semi-final spot for the eighth year in a row.