"Know your place first", Erdogan told the monitors in an address to supporters outside his vast presidential palace in Ankara.
A defiant Erdogan has dismissed complaints from his domestic opponents and European observers, saying the vote put to an end all debate over the powerful presidency he has long sought.
"Moving from rhetoric to action would be a clear signal that Turkey does not want to be a member of the European family", he insisted.
Turkey's main opposition party on Monday called for the annulment of the referendum, arguing it had widespread reports of voting irregularities.
There were protests in Istanbul with a few thousand people crowding the anti-Erdogan Besiktas and Kadikoy districts, blowing whistles and chanting "We are shoulder to shoulder against fascism".
The decision upholds the result of the landmark referendum, which has polarised Turkey in the last few months and highlighted the splits in a society that is still reeling from a coup attempt previous year and repeated terror attacks by Islamic State and Kurdish separatists.
Hurriyet said around 14 protesters were detained by the police in the Mediterranean province of Antalya, where a majority of people voted against the constitutional changes in Sunday's referendum.
Syrian children at a refugee camp near Gaziantep last spring.
The result laid bare the deep divide between the urban middle classes who see their future as part of a European mainstream and the pious rural poor who favor Erdogan's strong hand.More news: AIADMK rules out change in CM, Palaniswami to stay
He said that Turkey could hold a referendum on its long-stalled European Union membership bid following the criticism.
"If the package is implemented unchanged, this will have to lead to the formal suspension of the European Union accession talks", she added.
Erdogan earlier congratulated cheering supporters at Ankara's airport for "standing tall" in the face of the "crusader mentality" of the West.
"We will demand the rights of the voters until the end", he said. We talked about these things in general.
The White House said Trump and Erdogan during their phone call also discussed the war in Syria, which has complicated ties between the two countries, according to The Associated Press.
Observers from the Organization for Security and Cooperation in Europe (OSCE) and the Council of Europe said Sunday's referendum had been an uneven contest.
The parliamentary assembly of the Council of Europe (CoE) also noted that the referendum "fell short of CoE standards".
Turkey's foreign ministry dismissed the observers' criticism as lacking objectivity and impartiality.
"We look to the government of Turkey to protect the fundamental rights and freedoms of all its citizens", said the department's acting spokesman, Mark Toner.