Johnston believes assistant referee Stuart Stevenson should have awarded a goal with the score tied at 1-1 when a Michael Gardyne chip came down off the underside of the bar, before Thistle scrambled the ball away.
The visitors survived the scare and went on to clinch the points with an Aaron Taylor-Sinclair goal six minutes from time, to drag Kilmarnock into the fight to avoid the relegation play-off spot.
Johnston said: "It's a massive decision. I spoke to the referee and he said he couldn't see it so he couldn't make a decision.
"So he's relying on his linesman and I think it's him that's not given it.
"For him not to give it, it's a big decision when he's not in a good position either. I suppose they need to be certain but it looked over the line from where I was.
"The big decisions today didn't go for us. Some of the chances we had, even the save in the last minute from Ross Barbour, the goalie has pulled off a fantastic save. Those things change games."
Thistle manager Alan Archibald felt the three points were just reward for his team's ambition and will to win at Rugby Park.
Archibald's team responded positively to the 4-2 reverse to Hearts in their last game, to give them a fighting chance of staying up.
"They all wanted to win the game," Archibald said. "Sometimes you have to put the reins on them but they have a real hunger and desire about them.
"They deserved it for our full-back being in that position.
"It's a fantastic result and a fantastic reaction from our last outing.
"I thought first half we were very, very good. We had a hunger and desire from the off and they showed they wanted it.
"Kilmarnock had a spell when we gave them a couple of chances but I thought we deserved it."