Mbappe struck twice and created Eduardo Camavinga's goal for the win at San Mames.
Valverde said afterwards: "The best thing was the work we put in over the 90 minutes. For several games now, we've struggled to remain focused and we've conceded goals very early on. Today we said something very clearly in the dressing room, which was to try to change that and go out and press and score first, to give ourselves some breathing space.
“Today we played brilliantly. The whole team worked very well in defence. We were also very good in attack. We have key players who turn almost every ball they touch into a goal. We are delighted with the victory and I'm delighted to be part of this team."
On Mbappe's performance, he added: “It's crucial that a player of his calibre can, every time he touches the ball, finish the move with a goal almost every time.
"It is motivating for us, it's reassuring to have him up front, linking up and working with the team. We know everything he can contribute in attack, all the goals, but it's always good to see them defending him and Vini Jr. as they have defended.”