The rivalry between Barca and Real has always been fierce but it took on an added dimension last season when Mourinho questioned the integrity of the Blaugranas and the achievements of opposite number Pep Guardiola following the sides' Champions League semi-final first leg encounter.
Mourinho has since gone on to label Barcelona a "small team" and earlier this week said he had to search the internet to find information about their Champions League opponents, Plzen, suggesting that Guardiola's side had been drawn against easier opponents than his own team.
When asked about the comments, Alves responded by insisting he and his team-mates have grown tired of the Portuguese manager constantly discussing Barca.
"We know what he is like. He is always trying to take merit away from others," Alves said. "We will just get on with our work and don't want to get involved with any of that.
"We're inferior in that respect and we like to do our talking where we do it best - on the pitch. Journalists love it because it sells a lot of newspapers, but we are focused on performing on the pitch."