The 19-year-old defender started the first leg against the Valencia-based club, when Barca were beaten 2-1.
An Ousmane Dembele brace inspired a 3-0 win in the Camp Nou return but Levante appealed to the Royal Spanish Football Federation (RFEF) that Chumi should not have featured in the initial game after accumulating five yellow cards for Barcelona's B team in Spain's third tier.
Barca were convinced Chumi was eligible due to a rule change in November that suggests a player can feature for the first team in another competition as long as their suspension for the reserves is less than a two-match ban.
The RFEF ultimately rejected Levante's appeal against elimination because it was filed too late, but Valverde believes Barcelona should not be seen as simply benefitting from a technicality and called for clarity around competition rules.
"If you look at the competition rules we did nothing wrong. Some people may interpret the rules a different way.
"It needs to be made clear – not for the person who is writing the rules but for the people who are reading it.
"I think we have acted correctly and within the law."
On Levante's appeal, Valverde added: "No, we're not worried about this matter, but every club has to defend their interests.
"Levante will do what they think is correct and so shall we. We're just focusing on this game knowing we have another on Wednesday [against Sevilla in the quarter-finals]."
Leganes sprung a surprise when they beat defending La Liga champions Barca 2-1 in September – a match Valverde wants his players to remember as a warning.
"We played very badly," he said. "It was good during the week and we all had the feeling that we were going to win it but in a minute they scored two goals.
"We have to learn from that. For us it is essential to get the points and start the second round [of the season] well."