The Colombian gave Vini Jr his senior debut when coach of Flamengo.
Speaking with AS, Reinaldo said: "I'm very fond of him, and I think the feeling is mutual. Coaching him is one of the gifts football has given me.
"We have to try to channel (Vini's temper) it somehow. The experience will help him moderate that temperament.
"His attitude in the Clásico surprised me a lot. He's a good guy, and that behavior was strange to me. It hurt me a lot. He showed a great lack of mental and emotional control.
"I've been in a similar situation with a player before, and I know it doesn't lead to anything good."
Put to him that Vini is now 25 years old, Reinaldo replied: "That's precisely why he needs to control those outbursts. He was betrayed by the emotion of the moment. He's under immense pressure, which he puts on himself, but he can't act like this at this stage.
"He's mature enough. Hardly any player understands why they're being substituted, but the coach is the one in charge and makes the decisions. He needs to seriously reconsider."
Asked how Real coach Xabi Alonso must have felt, Reinaldo also said: "I'm sure it bothered him a lot. It was an adverse situation with a player of such high status, and it was in full view of the world, but his reaction was admirable. He showed his composure and maturity by distancing himself from the conflict and looking away.
"He handled it very intelligently to avoid further problems. A coach is always exposed to these situations because of the players' selfishness in always wanting to play and refusing to accept substitutions.
"This situation cannot be allowed to happen again. Vinicius is a role model for young players and has a leadership role at Real Madrid that he must exercise differently, never like this."