The somewhat unexpected result at Balaidos followed a 1-1 draw with Real Madrid the previous week.
Although the Basques are still in fourth spot and retain a four-point lead ove Villarreal, Valverde is determined for the team to return to the form they showed in January, in which they won three consecutive league matches, earning Valverde the Liga BBVA Coach of the Month award.
"It's always important to win games, but it's now even more important," the coach told a press conference.
"We've drawn two games in a row and to achieve the objective we've set our hearts on, which is maintaining fourth place, we have to pick up points and get back in a similar vein of form to the last four months."
Espanyol beat Athletic back in September, and Valverde is expecting another rough ride from the club he used to play for and coach.
He added: "We are expecting an abrupt match. Man for man they are a very difficult team to play against, they put you under a lot of pressure, and we will have to be prepared for that.
"They force you to play in a way which is not nice on the eye, we'll have to keep combatting their pressure and go into the game prepared for anything."
Ander Iturraspe will miss the game through suspension, a loss that Valverde said was "important because he's been playing very well recently and maintained consistency, but we expect our midfielders to be suspended from time to time".
Espanyol's only absentee is midfielder Victor Alvarez, suspended after getting sent off in the 1-0 win over Granada last weekend.
Espanyol coach Javier Aguirre was not particularly optimistic about his team's chances of becoming the first team to beat Athletic in the league at their new stadium when speaking in his pre-match press conference.
The Mexican said: "It will be an incredibly demanding game. Athletic put a lot of pressure on you, they never let their guard drop and as soon as they do their fans quickly pick them up again."
But he added: "Valverde knows this club very well and he knows we don't give anyone an easy game, that we are an intense team and that we always fight for every ball.
"Athletic never tire of running, but neither do we."