Turkey's referendum campaign was "unequal", with opponents suffering restrictions and state resources being misused, international monitors say.
Late changes in ballot counting marred the vote and removed a key safeguard, they added.
Turkey has called the comments biased. In the referendum, voters gave sweeping new powers to President Erdogan.
The narrow vote was ruled valid by Turkey's electoral body, despite claims of irregularities by the opposition.
President Recep Tayyip Erdogan's push for an executive presidency succeeded with 51.4% voting for it.
Despite saying that the voting day was "well administered", the Organization for Security and Co-operation in Europe (OSCE) and the Council of Europe criticised the campaign, saying:
◾It was an "unlevel playing field" and the two sides of the campaign "did not have equal opportunities"
◾It was unbalanced due to the active involvement of the president and several senior officials
◾It was tarnished by a number of senior officials equating No supporters with terrorist sympathisers
◾Administrative resources were misused
◾Under the state of emergency, essential fundamental freedoms were curtailed
◾Despite some measures, the legal framework remained inadequate for a genuinely democratic referendum
They also criticised a late change by electoral officials that allowed voting papers without official stamps to be counted. They said this move "removed an important safeguard and were contested by the opposition.
But the head of Turkey's electoral body, Sadi Guven, said the unstamped ballot papers had been produced by the High Electoral Board and were valid. He said a similar procedure had been used in past elections.
U.S. President-elect Donald Trump's choice to be national security adviser has suggested that Washington should improve its relations with Turkey by extraditing a cleric whom Ankara blames for a coup attempt in July.
Retired Lieutenant General Michael Flynn, the former director of the Defense Intelligence Agency whose appointment was announced on November 18, described Fethullah Gulen on his blog site for The Hill newspaper as "a shady Islamic mullah residing in Pennsylvania" who is hiding a "radical Islamist" agenda.
"Gulen's vast global network has all the right markings to fit the description of a dangerous sleeper terror network. From Turkey's point of view, Washington is harboring Turkey's Osama bin Laden," Flynn wrote on election day. "We should not provide him safe haven."
Flynn noted that Gulen followers have been donors to the Clinton Foundation, a global charity headed by the family of Trump's Democratic rival Hillary Clinton.
"It is time we take a fresh look at the importance of Turkey," he wrote. "We need to adjust our foreign policy to recognize Turkey as a priority. We need to see the world from Turkey's perspective."
In light of Flynn's comments, Turkish President Recep Tayyip Erdogan hailed Trump's victory as a "new era" in Ankara's relations with Washington and has stepped up demands that Gulen be immediately handed over since the November 8 election.
The Obama White House, to Erdogan's frustration, has said it will let the Justice Department decide whether there is any legal merit in Turkey's extradition request in what likely would be a long, bureaucratic process.
Gulen has never been charged with a crime in the United States, and he has consistently denounced terrorism, as well as the failed coup in Turkey, as have the schools and charitable organizations associated with him.
One of Gulen's lawyers, Jason Weinstein, called Flynn's comments about Gulen "troubling," but expressed confidence that the United States will continue to handle the matter fairly.
"We hope and expect that the law will be followed here and that politics will not interfere with the judgment of career officials at [the Justice Department]. If the law is followed, then we are confident that Mr. Gulen will not be returned to Turkey, where he is certain to be subject to torture, a sham trial, and execution," Weinstein said.
Turkey's President Recep Tayyip Erdogan has rejected criticism by monitors who say the referendum campaign fell short of international standards.
"Know your place," he said, adding that he did not accept the comments.