The first was for a foul on Miller and when the defender decided to argue the decision with referee Stuart Dougal, he was dismissed.
With Hibs down to 10 men Nish was brought on as a substitute, only to be sent from the field of play with nine minutes remaining for foul and abusive language.
Paatelainen was outraged at the actions of Gathuessi and Nish, saying: "If players talk to the referee then they are asking for trouble, it's as simple as that.
"Both players should know better and every player should know that if you start arguing with the referee then you will lose every time.
"I am surprised the referee went into the dialogue with the players and argued with them on the pitch.
"But Thierry Gathuessi was booked and he carried on talking, so there was only one solution after that."
On Nish's sending-off, Paatelainen added: "If you talk to the referee and call him names there are no excuses, our players should know better than that and it is disappointing."
Both Gathuessi and Nish are now facing being disciplined by their manager, who said: "We will deal with matters internally as always and we must make sure the players know better the next time."