The match was abandoned at half-time with the game goalless, the pitch deemed unplayable by referee Kevin Clancy after the relentless rain led to parts of the playing surface in front of the Jackie Husband stand becoming dangerous for the players.
Despite the game not being completed the booking will stand, and Archibald agreed with then-Inverness manager Butcher when he called for the authorities to address the rule after the abandonment of a match earlier in the season.
"I heard Terry mention it after the Ross County game, so I was aware of it," said Archibald.
"It's a really strange one. I think it's something they have to look at and maybe change.
"We've now got a booking and an injury (to Isaac Osbourne), so it's a sore one to take."
The abandonment denied Partick Thistle another chance to record their first home league win of the season, having failed to pick up a victory at Firhill in seven previous attempts since returning to the top flight.
"It's one of those things," said Archibald.
"I don't know when the game will get played now but we've got another massive game next week against Kilmarnock and we'll go down there looking for a victory."
The other booking in the match came for St Johnstone winger Gwion Edwards, and the Welshman's annoyance at finding out the booking will be upheld was further compounded as he felt the caution was unmerited in the first place.
"He's booked me for a dangerous tackle apparently," said Edwards.
"I was just jumping to block the ball, I didn't think I'd caught him but he must have seen something.
"A few of the boys were telling me (the booking will stand) in the changing room and I was a bit gutted about that. It's a bit harsh that decision but that's the rules I suppose and you've just got to get on with it."
St Johnstone had handled the swirling wind and sodden pitch rather better than the hosts, and although manager Tommy Wright understood the referee's decision to abandon the match, he could not hide his disappointment at what he perceived as a missed chance to go on and collect a valuable three points.
"I thought we were the better team. I thought we adapted to the conditions better, so from that point of view we're disappointed the game didn't continue," said Wright.
"But listen, the referee's got a lot of responsibility for player safety, and I would never, ever question a decision where he's put player safety at the top of the list."