Speaking in Brussels on Monday, Şanar Yurdatapan said more public criticism would send the "right message" to President Recep Tayyip Erdoğan.
Erdoğan has been attacked over his government's response to the coup, which has seen a crackdown on journalists, unionists and human rights activists.
European Parliament President Martin Schulz, on a recent official visit to Ankara, paid tribute to "all the Turkish citizens who courageously took to the streets to defend democracy" in the coup.
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This, said Yurdatapan, contrasts with some MEPs who have strongly expressed their concerns about the Turkish government response to the attempted coup.
Several deputies, including German member Elmar Brok, said that although they supported the EU-Turkey migration deal, the European Parliament could only give the green light to the visa liberalisation, which is part of the deal, once all of the 72 benchmarks have been met.
Speaking at the Brussels press club, Yurdatapan pointed out that thousands of people - including soldiers, judges and journalists - have been detained for questioning while some of them have also lost their job.
Yurdatapan was forced to live in exile in Germany for 11 years for past criticisms he has made of the Turkish authorities.
EU leaders, such as Schulz, should be "more vocal" on Turkey, said Yurdatapan, who was particularly critical of Erdoğan's treatment of Turkish journalist Can Dündar, who was jailed after the newspaper he edited published images showing Turkey was secretly sending arms to the Syrian war.
Yurdatapan, of the Institute for Freedom of Expression-Turkey, is also critical of the Turkish judiciary, telling this website, "The justice system in Turkey has never been truly independent but it has actually got worse since the coup."
The activist, who received the Global Human Rights Defender award from Human Rights Watch in 2002, added, "Erdoğan has taken advantage of the coup to do what he wants.
"The message I am trying to convey is that we need to raise public awareness of what is happening in Turkey right now."
Meanwhile, the European University Association (EUA), the body representing the higher education sector in Europe, has also voiced concern at the current situation in Turkey, an issue that will be discussed by MEPs at their plenary in Strasbourg on Tuesday.
"With 64 EUA member institutions and nearly seven million students, Turkey is an important part of the European higher education area," said EUA President Rolf Tarrach.
"It is in the interest of the entire sector to promote dialogue and to work together towards preserving the fundamental values that universities share."