Referee Brian Colvin pointed to the spot with after Dougie Imrie was brought down by Mark O'Hara and Paul McGowan stepped up to fire past Cammy Bell to cancel out Liam Kelly's opener.
Shiels felt the penalty award was harsh on his team, and threatened to refuse to comment on referees' performances until the officials themselves are put before the microphones.
"I have to watch what I say, Mark was unlucky. Lets put things into perspective, I'm the manager of Kilmarnock and I'm going to be biased towards my team," said Shiels.
"If you want me to speak about decisions in a game then interview the referee, I will talk all day long in response to what he has said.
"That's the way it should be, I will not answer questions about referees and I'm emphatic about that.
"I'm not doing any more interviews until the referees are interviewed.
"The conditions were really difficult for both teams and I was very pleased with the performance, we were in control of the game, but it was taken out of our hands - the penalty changed the whole shape of the game."
The Rugby Park boss also confirmed the capture of midfielder Ibrahim Rabiu, who has switched from Celtic to Kilmarnock after failing to become a first-team regular in Glasgow.
The Nigeria international could be unavailable until the beginning of February however, after being named in his country's squad for the upcoming African Nations Cup.