The Serie A side, one of the most feared teams in Friday's play-off round draw, will host Bilbao on August 19 in the first meeting of a two-legged encounter, with the return taking place eight days later.
While Rafael Benitez's side will start as favourites, Valverde is confident his squad has the quality to reach the group stage of Europe's premier club competition for the first time since 1998.
"It's true Napoli are a big side but it's a team we can beat and get through," he said. "We respect them because they are a strong side, but we have real confidence in our chances.
"We already knew we had to face important sides. Maybe Arsenal and Napoli were the strongest teams but to be honest if we want to be in the Champions League we have to face these kind of teams. We cannot be surprised now by that.
"Napoli are a really organised team. They are really strong at the back and it's difficult to catch them on a counter attack but at the same time they have a big talent in attack."
Bilbao, who finished fourth in La Liga last term, continued their preparations for the new season with a 3-1 victory over Borussia Monchengladbach on Saturday
Aritz Aduriz struck a first-half hat-trick in Germany, with Valverde's side also set to meet Olympiacos ahead of their initial contest against Napoli.
Valverde added: "These matches are important for us in order to prepare the tie against Napoli, but we are not thinking just about that Champions League tie because we have a La Liga match [against Malaga] in the middle of it.
"I know the main thing is now the Champions League but we cannot forget that La Liga match and we have to be ready too."
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