Fernando Alonso has accused Formula 1's governing body of "incompetence" and lacking knowledge of racing.
The Alpine driver identified incidents at the last race in Miami but also made an oblique reference to the FIA's handling of other issues this year.
He said he had seen no improvement at the FIA, despite its attempts to restructure following the handling of last year's finale in Abu Dhabi.
The FIA told BBC Sport the matter had been referred to the stewards.
Alonso described a penalty he received in Miami for gaining an advantage by going off the track as "unfair". The five seconds added to his race time for cutting a chicane dropped him out of the points.
He said he had immediately given back the time gained after the incident but the stewards had looked only at the fact that he had then gone faster in the next section of the track, and had failed to respond to Alpine showing them telemetry data to prove his point.
"We believe it was very unfair and incompetence from the stewards," Alonso said.
"They were not very professional. I missed one corner and gave back the time. They saw the pink colour [for fastest] on the next sector and took it without asking for proof.
"We arrived back with the proofs and they were packing up, not even in the room. We showed them the data and they found themselves with their hands tied because they had already issued the penalty. It was very bad. It is something that should not happen in F1 with the professionalism and the standards F1 has right now."
He also heavily criticised Niels Wittich, who has acted as race director at all five races this year.
Alonso pointed to Wittich's decision not to respond to drivers' requests for an impact-absorbing barrier to be installed at a corner where Ferrari's Carlos Sainz crashed heavily in Friday practice in Miami.
Sainz had complained in the drivers' briefing that the impact was far more severe than it should have been given the low speed involved, but was told it was a freak accident and a barrier was not necessary.
Alonso's team-mate Esteban Ocon had an almost identical accident the following day, which damaged his car's chassis.
Alonso said he expected Eduardo Freitas, who takes over as race director from Wittich for this weekend's Spanish Grand Prix, to be an improvement on Wittich.
Asked if he had seen evidence of improvement from the FIA following the restructure that came after former race director Michael Masi failed to apply the rules directly in last season's controversial championship finale, Alonso said: "Not."
"We saw a couple of things already that showed we still need to improve a lot," he added.
"You need to have some knowledge about racing before being a race director or trying to monitor a race and I don't think that knowledge is in place at the moment.
"There is a new race director here. Freitas has a lot more experience at World Endurance Championship and the top level and that will already improve things.
"Even the accident we had in Miami with Carlos and Esteban, we pushed to have some barriers there and nobody did anything. When you don't have that knowledge of racing, it is difficult to talk."
Ocon said he had spoken to Freitas in Spain this week and been told that after analysis of both accidents there would be changes at the Miami track next year.
Wittich has also courted controversy this year for taking a by-the-letter approach to the rules, which has led to drivers being told they cannot wear any jewellery in the car.
Alonso said: "We just need to keep improving that we are the only ones driving the cars and experiencing the crashes and when we feel something is needed, we should be listened to.
"In Miami and some other examples we didn't have that because it seems the focus is in another place."
Lewis Hamilton said in Miami that the new focus on jewellery and clothing was "almost a step backwards" and said the sport had "bigger fish to fry".
Asked about Alonso's comments, McLaren's Lando Norris said: "Fernando's a guy you would listen to in terms of the experience he has in racing. If he says what he says, he's probably got a bit of a point, at least."
Alonso's comments also come in the context of a widespread dissatisfaction among teams and at commercial rights holders F1 at some of the FIA's actions this year.
Among them were the decision by new FIA president Mohammed Ben Sulayem to delay approval of a plan for the number of sprint races to be doubled to six next year.
F1 is so unhappy it has been quietly exploring ways the FIA could be sidelined from running the sport, BBC Sport has been told.
Ben Sulayem went to see Alonso in the paddock during the course of Friday and they discussed the issues raised by the Spaniard.
Alonso said of the meeting: "I am very good friends with Mohammed. We all try to improve the sport and that is the aim for everyone."
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