"We can not let them get away with this", he said at the Soccerex conference in Manchester.
Several Spanish clubs, including Real and Barca, were punished past year for breaching rules on state aid but Tebas dismissed any comparison between those cases and the FFP breaches he was accusing City and PSG of.
"By contrast, Mr Tebas' statements are ill-informed and in parts pure fiction".
"Manchester City paid almost €1000m, PSG €950m for transfers".
Tebas recently wrote to UEFA urging them to investigate PSG and City and on Wednesday he repeated his view that City's spending on players came from "oil money".
"Manchester City paid almost £900m, PSG £868m for transfers, If we don't control the situation the whole industry will become destructured".
UEFA did announce last week that PSG are being investigated but Press Association Sport understands that was not prompted by La Liga's complaint and City are certainly not being looked at.
City, who spent more than £200m in the summer transfer window, offered Arsenal £55m up front for the Chile forward on Thursday but a deal failed to materialise.
He said: "If I remember correctly, PSG and Man City were sanctioned, but then the sanction was somehow reduced in some odd agreement that was not made public".
PSG have been owned by Qatari Sports Investments (QSI) since 2011 and Tebas claims clubs with mega-rich owners have an unfair advantage over their rivals.
The City Football Group (CFG) added: "As you would expect, Manchester City Football Club and the City Football Group are seeking appropriate legal counsel and will act accordingly on that advice". "That is impossible. This is financial doping". "If [Neymar] had gone to Manchester United maybe I would not have gone to the courts because this is not financial doping and maybe they have the money to buy this player". "Because there is a value coming from sponsorship outside of the market".
Neymar is one of the crown jewels in world football, both as a player and a commercial force, and neither Barcelona nor La Liga are happy that he was lured away against their will. We believe the European Union need to investigate, too. "This is not football's market price, It's gas market price".
"They are laughing at the industry aren't they?"
"I think the buyout is higher but if Nasser [Al-Khelaifi] wants them they can just open the pipes and afford them", Tebas conceded, referring to QSI's chairman Nasser Al-Khelaifi.