The visitors twice took the lead at the Parc des Princes before Blaise Matuidi's goal in stoppage time rescued a draw for the Parisians.
However, it was the home side's first equaliser that upset Alves and his teammates as ex-Barca striker Zlatan Ibrahimovic appeared to clearly be in an offside position when he prodded home after Tiago Silva's header had come off the post.
"We cannot complain, but the people that are outside and cannot be banned, they have to complain," he told a press conference on Wednesday.
"It is not possible that they cannot see someone is two metres offside. We are not slow or stupid. I am not going to put on a brave face like other people do."
Referee Wolfgang Stark was heavily criticised in 2011 by Real Madrid manager Jose Mourinho after he sent-off Pepe for a challenge on Alves in a Champions League semi-final between the two.
And the Brazilian thinks the German official was under extra pressure because of Mourinho's insinuations that Barca often get favourable decision in big European games.
"The referee was under a lot of pressure. The players are the protagonists and when they are not the ones talked about it is because something bad has happened.
"The pressure I refer to with the referee is what Mourinho said about Stark."
"Protests influence the refereeing. The referee thinks if he gives something or doesn't give something, the managers are going to criticise him.
"Sometimes we are too good and because of this these type of things happen.
"I come out here to speak about it and I am the bad guy, but we are in a country where you are not allowed to have an opinion and I speak freely.
"We need to have a little more nastiness when it comes to protesting, if we don't they treat you as if you are stupid."