Athletic handled Mikel Jauregizar's red card to win as Oihan Sancet, Nico Williams and Aitor Paredes struck for the visitors.
Valverde said: "It was a very important game for us. We had taken it as a test because we had lost a match in the last minute. I think we dominated it, but the expulsion has made us have a different match ahead.
"When you win, it always leaves you with a much better taste. I thought I would have made some changes to solve the problem of our two midfielders with yellow cards, but before doing so, they sent off Jauregizar.
"When they create scoring opportunities for us, I always think it's the opponent's merit. Here it's about making your own strengths prevail. I've seen danger in both places. The games last 90 minutes and at half-time we already saw that things could change.
"They had a lot of spirit and with the third goal we had room to hold on and get three points in a very important week for us."
"We have spent two weeks mulling over the last play of the match against Atlético, in which we lost the points. This victory in a week with three games will be fundamental to not get left behind, to stay in those positions and to look forward."