That's according to Argentine journalist Gaston Edul who is renowned for his relationship with his players in Argentina and the rest of South America.
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Conte parted company with Spurs late on Sunday night, bringing an end to a prolonged period of uncertainty over his future.
His parting shot was to take aim at the club's players following their 3-3 draw with Southampton before the international break, an outburst that looked to be the final straw in his turbulent tenure.
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Those comments about the squad clearly had quite an impact on the players, with Edul revealing just how frustrated Romero and Richarlison actually were under Conte.
Discussing the situation, Edul told TyC Sports: "Conte's relationship with the squad was very bad, it's needless to say, it's something that we could see in his words.
"Some players had given an ultimatum in case he continued. Now the outlook of Tottenham changed."
Asked if a player issued an ultimatum, Edul said: "Yes, I say that because we can say it, in fact we waited to say it.
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"Cristian Romero was rethinking about his stay at the club if Conte remained.
"As I understand it, the same thing happened with Richarlison.
"Because he treated them very badly, not only face to face or in a private environment but also publicly.
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"Conte publicly criticised the players and that caused friction. But now Romero is going to stay at Tottenham, that's the plan."
Conte's second in command, Cristian Stellini, will take the job until the end of the season, alongside Ryan Mason.