Coutinho was brought off the bench at half-time and within four minutes he had converted former Liverpool team-mate Luis Suarez’s cross to open the scoring.
Ivan Rakitic then added a second to seal their place in the final, but it was the early introduction of the Brazilian which was the catalyst for the victory.
“It normally takes a little longer to make the changes,” Valverde admitted.
“But we saw it very clearly, we had to try to move the top part a bit.
“Andre [Gomes] was helping us with his strength to be together up and back, but I saw that with the domain we had we needed a player who could bargain at the last moment.
“And the play went well.”
Valverde also admitted that he is excited at the chance of winning his first piece of silverware since taking over at the Nou Camp in May.
"I am very excited,” Valverde added.
“I suppose like any coach, to play the cup final with your team and have the chance to win a title, knowing the Barca demand to win always.
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