Partick Thistle manager Ian McCall described referee Scott Lambie as "way out of his depth for this level of football" after defeat in Inverness.
Caley Thistle move level on points with the Scottish Championship leaders after Billy Mckay's second-half winner.
The visitors had been reduced to 10 men after midfielder Kyle Turner's studs-first tackle just before half-time.
But it was the denial of a penalty for a 26th-minute challenge on midfielder Ross Docherty that angered McCall.
Thistle had Aaron Muirhead and Kevin Holt to thank for goalline clearances at opposite ends of the game, while a couple of saves from visiting goalkeeper David Mitchell looked to have denied the hosts until Mckay drilled home from 12 yards.
It means the Glasgow side are now only top virtue of goal difference after the hosts stretched their unbeaten run to five games.
Queen's Park, who are one point behind, could go top when they visit Ayr United, who could draw level with the top two themselves, on Saturday.