Referee Stevie O'Reilly adjudged Brian McLean had handled in the area in the 45th minute, after Kenny Deuchar headed back towards goal from Danny Grainger's cross.
Liam Craig tucked home the equaliser - his ninth goal of the season - from the penalty spot before Deuchar, like Craig a former Bairn, profited from a Tam Scobbie mistake to snatch the win the game after 84 minutes.
Marc Twaddle had earlier given Falkirk the lead before O'Reilly made Pressley's blood boil.
He said: "It's a tough one for us all to take. Obviously, I'm very, very angry at the decision made by the referee on the stroke of half-time.
"It was a game-changing decision, a big call and a decision he gets wrong. I thought there was absolutely no intent by Brian McLean to handle the ball. It angers me he made such a big call at a crucial time.
"I think for referees we are an easy club at this moment in time to make decisions against, because not enough is made of them.
"If the Old Firm get a penalty against them then it's back-page headlines.
"(But it's) easy to make decisions against Falkirk - no real repercussions, no discussions on it. That has to change.
"We can't accept what we got today, no way. No way can we accept being an easy target for referees.
"If I'm hauled up, so be it. I'm extremely angry and angry for my players who put so much into it.
"In terms of penalties against us, it seems to be a club that referees find easy to give penalties against. That has to change."
Pressley's side are now 11 points behind Saints and face a growing fight to overhaul the likes of Hamilton and St Mirren to stay up.
He added: "We just have to continue to apply ourselves in the right manner, pick ourselves up and not feel sorry for ourselves. I can assure you we will come out fighting next week for the Hamilton game.
"Probably on reflection a draw might have been a fair result, up until their goal I thought we fully merited the lead."
On Scobbie's error, after he allowed Deuchar to lob home in failing to deal with a long ball, he said: "It's a disappointing goal. Every goal you lose is disappointing.
"We must react in a positive manner this week; we must come out fighting next week. That for me is the biggest thing: the reaction."
St Johnstone manager Derek McInnes disagreed with Pressley, feeling it was a spot-kick.
He said: "My initial reaction was a penalty kick, I shouted for it.
"I thought the referee had a really good view of it.
"We have been on the wrong end of a lot of poor penalty decisions this season as well, but I thought that was a penalty. Credit Liam for putting it away, he still had that job to do and he has done that well this season."
McInnes' side went a long way to securing SPL survival with a key win and still boast games in hand.
He added: "There is a thin line between winning and losing, as we found to our cost last week, losing a late goal against Motherwell.
"I said at the start of this week, this was as important a game (as any) in my career as manager at St Johnstone and I wanted the players to realise the importance of that.
"The crowd came down in their numbers for us, which I was absolutely delighted with. When they give us that type of support, they were brilliant today, we very rarely let them down.
"I was delighted the players managed to win the game, especially after coming from behind. There wasn't a lot in it but I thought we did just enough in the second half to win it."
Source: Team Talk