Real are now ahead of Barca at the top of the Spanish Liga lead.
"We know what he is like, we know that he tries to discredit others and we do take any notice of it," Alves said.
"What is certain is that we have to continue to do our own thing.
"We cannot compete on that level because we are inferior, so where we can compete we try to do things as well as we can and that is on the pitch with the ball.
"Then, off the pitch if were to enter into this competition we would lose for sure because we are a long way below in this aspect."
Alves believes that Mourinho deliberately looks to push the spotlight onto others and that he knows the media will give him the headlines he craves.
"Everyone has their way of acting and reacting, but the people that do this all the time are happy because they are being provocative, selling newspapers and are pleased with that," he continued.
"We have never and will lever do that because know what we want. We know where we are best and where we can compete and that is where we focus on being stronger."