The former Barcelona boss' departure was confirmed on Friday (AEDT), two days after the 2010 world champion was eliminated by Morocco on penalties in the last 16.
Luis Enrique's contract was due to expire at the conclusion of the finals, and the Royal Football Federation (RFEF) opted not to renew his deal and announced current Under-21 boss Luis de la Fuente is set to take over.
Former Spain boss Clemente feels Luis Enrique, who he coached at the World Cup in 1994 and 1998, should not be blamed after overseeing a second successive last-16 exit, having fallen at the same stage to host nation Russia four years ago.
"I think it is not a success to have dispensed with Luis Enrique as coach," he said. "This is yet another mistake.
"Luis Enrique is a very good coach, with his ideas, with his personality, friendly, pleasant, man of the house. The problem of the Spanish team is a problem of Spanish football.
"[Morocco] stood up and closed well behind, and the players did not have the temperament to overcome it.
"You always talk about the coaches, but when you play badly, you also have to talk about the players. Is Luis Enrique to blame [for the penalties]? Not really.
The RFEF is expected to officially announce De La Fuente as Luis Enrique's successor on Tuesday.
The 61-year-old has spent close to a decade coaching Spain's age-grade sides, winning the Under-19 European Championship in 2015 and the Under-21 equivalent in 2021.
He also took charge of the Under-23 side at the Beijing Olympics last year and won a silver medal following defeat to Brazil in the final.
"You don't imagine he'll end up as a coach," said Clemente, who coached De La Fuente at Athletic Bilbao during the early stages of his playing career.
"I think it's good, he's been in the Under-21s, and he's had good results. He's done well, he already knows the kids. I don't know how he coaches, but I tell you he's very good because he's a friend of mine."