The Basque club has lost seven of 15 fixtures in all competitions this season and have yet to taste victory in the UEFA Champions League ahead of Wednesday's clash with FC Porto.
Porto lead Group H with seven points having accounted for Bilbao 2-1 on the last matchday, while Valverde's men are bottom of the standings with just one point on the board.
But speaking after Sunday's win against Sevilla, who were sitting second in La Liga before their loss in Bilbao, Valverde argued that successful result should make his team more "relaxed" as they aim to turn their fortunes around in the Champions League.
"They're [Sevilla] a very strong team. It was a well-contested game that the viewers will have enjoyed," Valverde said, according to AS.
"We were very good, especially in the first half. We were defensively strong and had good chances for goals.
"They tightened up and we didn't score as many as we would have liked but it showed the value of the points.
"Now we're happier and more relaxed because we have beaten a great team. Hopefully, beyond the points, the win drives us on to reach our expectations and commitments."
Two weeks ago, Porto trumped Bilbao 2-1 thanks to goals from Hector Herrera and Ricardo Quaresma, while Guillermo Fernandez scored for the Spanish visitors to the Estadio do Dragao.
That result was Porto's first of three consecutive wins, following their Taca de Portugal loss to Sporting Lisbon, with league triumphs over Arouca (5-0) and Nacional (2-0) following.
Porto coach Julen Lopetegui - himself hailing from the Basque region of Spain - has warned his team not to lose focus despite their unbeaten start in the Portuguese Primeira Liga and the Champions League.
"We have to retain this ambition to get what we want," he said after the win over Nacional.
A win for Porto in Bilbao will see Lopetegui's men secure a berth in the next round of the Champions League.
Algerian attacker Yacine Brahimi will be the danger-man for Bilbao with the Porto midfielder having scored against Nacional, while he struck a hat-trick in the Primeira Liga outfit's 6-0 demolition of BATE Borisov at the start of the Champions League group stage.
"Brahimi gets better with each passing day and I am sure he will keep evolving, becoming an even more complete player," Lopetegui said.
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