The union announced its intention to strike on Tuesday in response to growing crowd violence and had support from 10 of the 16 clubs and the international players' union FIFpro.
However, PSAP said in a statement on Thursday it was unable to call a strike because Panionios, Asteras Tripolis Olympiakos Volos, Corfu, Kavala, Ergotelis decided not to take part.
"An essential and necessary condition to implement our action was the participation of the other teams which unfortunately did not want to join our effort for their own reasons, reasons which we do not understand," it said.
"We regret that those six clubs decided not to follow us and we also express our disappointment that there was no response from the Hellenic Football Federation, the Super League and the television channels covering the games of the championship."
The statement added: "It should be noted that the decision of PSAP, its players and the 10 clubs is a measure of responsibility and respect towards the Greek fans, all the players and the institution of the championship for which we at least understand that they should be protected... the message we wished to get across was received by all."
Violence inside and outside stadiums has been a constant problem for Greek authorities this season.
The top clubs, Olympiakos Pireaus and Panathinaikos, have been punished with supporter-bans after ugly pitch invasions involving battles with police and attacks on players.
The country was left shocked on Feb. 19 when hundreds of fans invaded the pitch following Olympiakos's tempestuous 2-1 win over closest rivals Panathinaikos.
Olympiakos supporters threw punches and kicks at the visiting players and battled with police in what was the fourth pitch invasion in Greece this season.
Attacks by supporters on the Super League offices and the home of Olympiakos player Vasilis Torosidis followed.
Panathinaikos assigned bodyguards to several players as the fall-out continued from what has been dubbed the "derby of shame" by Greek media.
Olympiakos can claim their 38th league title with a victory at PAOK Salonika on Sunday. They are 13 points clear of reigning champions Panathinaikos with five matches left.
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