Dede was dismissed with the use of VAR after his attempt at a header saw him miss the ball and catch Andrada in the 75th minute of the Copa Libertadores quarter-final first-leg clash at La Bombonera.
Menezes' men were trailing to Mauro Zarate's first-half strike when the Brazil centre-back was given his marching orders, and Pablo Perez's effort eight minutes from time clinched a 2-0 win for the Superliga side.
The Cruzeiro boss was unimpressed with the decision to send off Dede and asked the Brazilian Football Confederation (CBF) to provide greater protection to their teams.
"We have VAR so we do not have great injustices in football, and we saw a great injustice. We lost a player in our best moment of the game," said Menezes, who highlighted how CONMEBOL has dealt with ineligible players in the Libertadores this season.
The governing body awarded Independiente a 3-0 win over Santos after the Brazilian side fielded Carlos Sanchez in their last-16 first leg despite a suspension, while Boca and River Plate avoided punishment for selecting Ramon Abila and Bruno Zuculini respectively despite bans.
"Someone who wasn't on the field thought something was different. No Boca player did – so much so that they thought it was something against them," added Menezes.
"The referee made the decision and he is to blame for everything that happened.
"The referee wanted to dismiss Dede, and the problem is there are a lot of things against Brazilian teams. There was the case of Santos, the lack of punishment applied to River and Boca. Things are very different.
"It's something that doesn't smell good. I think the CBF and other federations have to take a stand. This is something serious. It has to be treated by Brazilian clubs seriously."
Andrada is expected to miss the Superclasico between Boca and River at La Bombonera and Guillermo Barros Schelotto backed the process behind Dede's dismissal.
"They must have had some reason for the red card," the Boca manager said. "There is the referee on the pitch and another three watching the VAR, and I think the situation is very clear, they will have had a reason to throw Dede out.
"When we play with VAR we have to respect the law more than ever because not only is there the referee on the pitch, but there are also three others out watching everything that happens."