PSG's bid to reach back-to-back Champions League finals came to an end at the hands of Manchester City, which won 2-0 to progress to the tournament decider for the first time in its history, 4-1 on aggregate.
Riyad Mahrez scored twice for City as PSG ended the second leg with 10 men after Angel Di Maria was red carded for kicking out at Fernandinho in the 69th minute.
Verratti and Herrera reacted angrily to the decision to send off Di Maria in Manchester, where PSG became just the third team to receive a red card in both legs of a Champions League semi-final after Deportivo La Coruna-Porto (2003-2004) and Lyon-Bayern Munich (2009-2010).
After last season's runner-up PSG was left licking its wounds, star midfielder Verratti and team-mate Herrera hit out at Kuipers.
"The referee told me 'f*** you' twice," Verratti said. "If I do that, I get a 10-match ban. Of course I talk a lot with the referee, but I never say f*** you."
Herrera added: "We talk about respect with the referees. The referee tonight said f*** to [PSG midfielder] Leandro Paredes.
"If we say that, we get a three or four-match ban."
PSG failed to land a single shot on target against City – the first time the French side has failed to do so in a Champions League game since 2003-2004.
"We were the best team for 70 minutes," said Herrera. "We attacked, we created problems for a team that is playing very well.
"We can leave with our heads held high. We are of course sad. It is not easy to do so, to be a semi-finalist. We must not change what we did today. We played well. We did everything. There are always things to improve."