"The silence is media-perceived," Quevedo said in a news conference on the second day of the World Apostolic Congress on Mercy (WACOM).
Quevedo explained that the Catholic Bishops' Conference of the Philippines (CBCP), in mid-2016, already issued a statement about illegal drugs and extrajudicial killings.
He said the CBCP also told individual bishops "that they can issue their own pastoral statements in their own dioceses." He pointed out that "many bishops have followed that."
The bishops have also encouraged laypeople to collaborate with the Catholic hierarchy in relation to the CBCP statement on drugs and extrajudicial killings.
This comes as more than 6,200 people have died in the war on drugs waged by the Philippine government.
Quevedo added that "we should think of the Church as not the bishops only."
The cardinal said: "Let the people do the action. We give the moral guidance. There has been a deliberate choice on that issue. Let the bishops give moral guidance, and let the people act. That's the Church."
Also during WACOM, Manila Auxiliary Bishop Broderick Pabillo urged Catholics to speak out on the recent drug-related killings in the Philippines.
In a speech, Pabillo said, "Can we now keep our mouths shut when more than 6,000 of our poor people are being killed on the mere pretext of drug trafficking?"