The referendum on a constitutional reform package on Sunday took place on the 30th anniversary of the coup led by Evren, now an ailing 93-year-old.
After the military seized power, about 50 people were executed, hundreds of thousands were arrested, many were tortured, hundreds died in custody and many disappeared.
Prime Minister Tayyip Erdogan reminded Turks of the repression that followed the military takeover as he campaigned for approval of the reforms, which rewrite a charter first drawn up when the generals held sway.
Erdogan promoted the reforms as a way to strengthen democracy, press Turkey's bid for membership of the European Union and ensure the army never dares overthrow another elected government.
Turkey suffered three coups between 1960 and 1980, and in 1997 the army persuaded an Islamist-led government to resign.
The military has seen itself as a guardian of secularism and the unitary state in the republic founded by Kemal Ataturk in 1923 out of the ruins of the Ottoman Empire.
Evren has defended the coup, saying military intervention was needed to bring an end to years of violence between left-wing and right-wing factions in which about 5,000 people were killed.
Among the 26 amendments approved by the plebiscite was a measure annulling an article blocking legal action against Evren and other leaders of the coup.
Rights groups leapt into action on Monday, filing petitions in Ankara, Istanbul and Izmir calling for Evren and at least two other coup leaders to be tried.
"This is a request that the chief prosecutor's office open a criminal case against Kenan Evren over crimes against humanity," the Human Rights Association said in a petition filed with the Ankara chief prosecutor's office.
Some legal experts have argued that a statute of limitations would prevent the coup leaders being put on trial.
Evren became president in the wake of the coup, a position he held until 1989.
He has spent his retirement painting on Turkey's southern coast. He came to Ankara to vote in Sunday's referendum.
It is common currency among Turks that the US Central Intelligence Agency played a part in destabilising Turkey in the late 1970s to pave the way for a military takeover in its frontline Cold War ally.
Surveys show an abiding mistrust of the United States in Turkey, partly because of perceived meddling in Turkey's internal affairs in the past.
About 58 percent of Turks voted in favor of constitutional reforms proposed by the government. Opponents had argued that some of the changes would result in the AK Party gaining influence over the judiciary.
