"Late changes in counting procedures removed an important safeguard", said Mr Preda, who headed the PACE delegation, referring to the election authorities' decision to permit ballot papers without an official stamp.
The constitutional reforms were set to grant more power to President Recep Tayyip Erdogan.
After the vote, Mr Erdogan repeated his intention to review Turkey's suspension of the death penalty, a step which would nearly certainly spell the end of Ankara's European Union accession process.
Turkey's constitutional amendments referendum campaign was dominated by the "yes" camp in media coverage, the Organization for Security and Co-operation in Europe's (OSCE) observer mission said in its turn.
But even as Erdogan's supporters set off fireworks to celebrate their victory, Turkey's main opposition party said they will challenge numerous votes.
The opposition alleges the vote was stained by violations.
The European Council recognized Turkey as a candidate for full membership in 1999 and negotiations were opened in 2005, but have since been suspended over concerns of authoritarianism in Turkey. But the main opposition CHP, which led the No campaign, has said it would contest the results.
The head of the country's electoral board confirmed the win shortly after Mr Erdogan spoke and said the final results would be known in 11-12 days.
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Erdogan raised the idea of bringing back capital punishment after last year's failed coup, suggesting it would bring justice to the families of the victims.
Germany, home to the largest number of Turks outside Turkey, said the apparent closeness of the result highlights a deep division in the country.
Leader Devlet Bahceli, who led the party's push for "Yes", said the result was an "undeniably successful achievement" and should be respected, according to Reuters news agency.
French leader Francois Hollande echoed the call, but added that France will follow observers' guidance as to whether the vote was free and fair. The result leaves Turkish society even more polarized and may produce more instability.
A European Commission statement urged the Turkish government to "seek the broadest possible national consensus" in the implementation of the constitutional changes, given the close result.
Under the changes, most of which will only come into effect after the next elections due in 2019, Turkey's governance will be transformed from a parliamentary system to an executive presidency.
Under the proposals, the office of prime minister would be abolished, allowing the president to draft the budget, declare a state of emergency and issue decrees overseeing ministries without parliamentary approval.
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