Ronaldo initially played on after being patched up on the side of the pitch and scored Real's 21st-minute opener in a 2-1 victory. But he had to be replaced at halftime after suffering problems with his vision.
"It was an accident, at no time did I try to cause harm to Cristiano Ronaldo," Navarro, who has a history of violent conduct, said on Levante's website.
"These are things that happen during a game and I regret having wounded him, but I repeat that it was something completely involuntary," the 32-year-old added.
Navarro had contacted Ronaldo on Monday to ask after his well-being and wish him a speedy recovery, Levante said.
Marca sports daily and other Spanish media published videos on their websites on Monday showing previous incidents involving Navarro, including a mass brawl he was involved in after a Champions League game between his former club Valencia and Inter Milan in March 2007.
Navarro punched Inter midfielder Nicolas Burdisso in the face, breaking his nose, and was banned for seven months by governing body UEFA.
Other incidents include an horrific studs-up challenge on former Real Madrid midfielder Luis Figo and an off-the-ball stamp on Barcelona forward Lionel Messi's ankle.
Ronaldo will miss Portugal's friendly in Gabon on Wednesday as a result of the wound, the country's football federation (FPF) said on Monday.
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