Johnston believes Kris Boyd was wrongly penalised for a foul on Russell Anderson as he lobbed the ball over visiting keeper Jamie Langfield and into the net in the 12th minute at Rugby Park.
However, referee Craig Charleston disallowed the goal and the Dons went on to grab an 82nd minute winner.
Johnston said: "If you're going to give free-kicks for that, you would be stopping play every two seconds.
"Boydy just simply outmuscled him and it's a great finish after that.
"The ref felt it was an unfair challenge but it looked a definite fair challenge to me as it did to the majority of the crowd judging from their reaction.
"It's a big moment and refs have got to get these decisions right because it changes games."
However, Aberdeen boss Derek McInnes disagreed following his team's 1-0 triumph: "It's a foul every day of the week.
"If Kris Boyd goes in with his shoulder and Russell falls down then that's different.
"But there was an arm on the back. It's not a shove but there's a weight there. I think Kris Boyd just leans in a bit too early."
Dons substitute Nicky Low was dismissed in the dying stages for a foul on Sean Clohessy and McInnes felt he was harshly punished.
"He over-ran the ball and in his enthusiasm to make up for it he has just half slipped - there were players slipping all over the place today," he said.
"He lost his footing and kind of lunged but he has pulled out at the death and almost stopped himself.
"I think a wee bit of understanding (was needed) from the referee.
"It was just youthful exuberance and desperation to play his part in the game."