Referee Kevin Clancy called a halt due to treacherous conditions in Maryhill, where torrential rain had rendered the pitch unplayable.
The game was goalless at the interval, and Clancy feared the playing surface would cause injuries if the action continued after the break.
"The ultimate factor for us was player safety," said Clancy. "It's of paramount importance when you're having to take a decision on the condition of the park.
"We felt, certainly as we were approaching half-time, that there were parts of the park, one corner in particular, where the ball wasn't rolling properly.
"It was sticking when it was coming out of the air and some players were even over-running the ball and it was ending up behind them, so it has the potential for ruining the match, but also causing an injury to a player if it was misjudged.
"We felt before the match that the pitch was playable, I had a word with both managers to discuss the conditions on the park, but as we were approaching half-time with the relentless rain, areas of the park were getting worse and some of the players were expressing reservations and concerns from both teams.
"Parts of the park had simply become unplayable."
Partick manager Archibald admitted he made a mistake in agreeing to start the match, as Isaac Osbourne picked up an injury and Gabriel Piccolo was booked in the 45 minutes.
"We've now got a booking and injury, so I would probably say now that it shouldn't have started," said Archibald.
"We've always had problems at Firhill over the years with that area of the pitch, but we had done a lot of work on it over the summer and we thought we'd done enough.
"As players and managers you just want the game to go ahead. Before the game I was saying 'get the game on' as well, but now the downside of that is we've got injuries.
"The referee said that it was difficult for our right-back [Jordan McMillan] and the wide player for St Johnstone [Gwion Edwards], because you didn't know where the ball was going to land and when it did land it just stopped.
"So it was probably the right decision."
St Johnstone manager Wright added: "We had it explained to us before the game that he thought the pitch was playable, and I think it was, but as the half went on, particularly the far side got worse," said Wright.
"He (Clancy) said he would assess it as the game went on, that's what he's done and he's made the correct decision.
"I thought we were the better team. I thought we adapted to conditions better, so from that point of view we're disappointed the game didn't continue.
"But the referee's got a lot of responsibility for players' safety and I would never question a decision where he puts player safety at the top of the list."