Josh Maja converted the penalty to put his side 2-0 up after George Dobson had earlier diverted Isaac Price’s drilled free-kick into his own net.
In addition to his concerns around the spot-kick against James Morrison’s side, Parkinson also raised concerns over the treatment of striker Sam Smith.
Parkinson added: “The second goal is a huge lift for them. You need help from referees and when you get a referee who’s refereed at the top level, you expect better.
“I have briefly (spoken to the referee after the game) and the other thing I’m getting very frustrated with is the treatment Sam Smith’s been getting.
“Watford away, the amount times he got hauled to the floor, blocked and body-checked. I sent all the incidents to the head of the referees and he agreed with me on nearly every one.
“We then go to Sheffield United and [Japhet] Tanganga pulls him down which is a straight red card and the free-kick gets given against Smudge (Smith).
“Today, there’s a slide wall pass which is putting him clean through and [Nat] Phillips just tugs him. It’s only slight contact, but it’s a red card and I feel Smudge needs more protection.
“I’m going to send all those instances together and ask the referees over the next two days to give me some answers because he’s had some bad decisions against him, Smudge.”
West Brom’s interim boss Morrison said he felt the penalty decision was justified given his previous talks with match officials.
“The referees at the start of the season said they were going to punish that. I’m yet to see it, so I’ll take it all day,” he said.
“I did feel that he (Kabore) was pulling Jayson, so correct decision.”
But Parkinson added: “I’m always in communication with Kevin Friend, the head of the referees, because he’s a great guy and he listens.
“But when the ref reviews those instances tonight, he’ll know I’m right and he’s wrong.”