They said Erdogan can now set the agenda for a European Union which dislikes doing business with a man who wants to join the bloc but also flouts its rules on human rights and press freedoms.
"The EU will be forced to swallow its pride and pander to the hubristic ego of President Erdogan," Natalie Martin, an expert on Turkish politics at Nottingham Trent University in Britain, told AFP.
"In so doing, it will be dealing with a government which may be democratic but is certainly not liberal and which will demand a high price for its cooperation."
Turkey is a longstanding candidate country for European Union membership but talks have stalled, largely on concerns over its human rights record which critics say went from bad to worse during the election campaign.
Yet in recent months Brussels has been wooing its Muslim-majority neighbour in the hope it will help resolve the Syrian war and stem the flow of hundreds of thousands of refugees and migrants fleeing the conflict.
The EU issued a surprisingly terse statement on Monday, saying that it looked forward to working with the new Turkish government -- but stressing that it awaited an OSCE observer report on the vote.
Brussels notably avoided directly congratulating Erdogan, his Justice and Development Party (AKP) which won 316 seats in the 550-member parliament, or Prime Minister Ahmet Davutoglu.
The OSCE said Monday that the conduct of the ballot was hindered by violence including a huge suicide bombing at a peace rally, and a crackdown on the media.
Critics and the opposition said Erdogan manipulated the press crackdown and a bloody new campaign against Kurdish rebels to convince voters frightened by the upsurge of violence.
- 'Lamentable cynicism' -
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Erdogan rejected the charges, saying he alone could ensure national security at a time when the Syrian conflict has stoked regional tensions and forced more than two million refugees to seek safety in Turkey.
Anne-Marie Le Gloannec of the Sciences Po institute in Paris said that the EU had got itself caught between needing Turkey to solve the migrants crisis and holding up membership on its rights record.
"You cannot make membership harder and harder ... and then ease off for this supposed democracy -- that is just lamentable cynicism, just because you need it to help you cope with a flood of migrants," Le Gloannec said.
But other analysts said that a stronger, more confident Erdogan might just see some merit in compromise.
They noted in particular how the president has played hardball with Brussels on plans to control the migrant flows to Europe via Turkey in return for increased aid and speeding up the accession talks.
Marc Pierini, visiting scholar at Carnegie Europe in Brussels, said of the refugee crisis: "Perhaps it is time for both to stop this bazaar diplomacy, this 'I do this, you do that diplomacy.'"
Sinan Ulgen, also of Carnegie Europe, said he expected a strengthened Erdogan "to revitalise the peace process (with Kurdish rebels) from a position of strength... which would help ease relations with the EU."
Ulgen also cited the possibility of progress on Cyprus, long divided between a Greek Cypriot south and a Turkish-backed north.
Ian Lesser, executive director of the German Marshall Fund's Brussels office, said Turkey's international partners would view the vote with "ambivalence mixed with wariness" in light of Erdogan's track record.
"Turkey's European and American interlocutors are going to be looking very closely whether this election result simply reinforces those tendencies or allows Turkey to somehow turn a page," Lesser told AFP.
"Europe and Turkey have a lot of business to do together."