Dr Helmut Marko says the remainder of the fierce 2021 title battle will now become "even more tense".
Mercedes' Lewis Hamilton clashed with Red Bull's championship leader Max Verstappen at Silverstone last Sunday - and Marko says Red Bull has now retained a lawyer to look into whether they can pursue a harsher penalty.
"He (the lawyer) has to look into what is possible in such a situation, within the framework of the existing sporting laws," the 78-year-old Red Bull official told Kronen Zeitung.
"We can't just let this go. It was really lucky that nothing serious happened to Max. The car and probably the engine are scrap. That can't be.
"A race suspension would be just," he insisted.
"It was an irresponsible act by him. Hamilton needs to know what the consequences are. A race suspension would be just."
Relations were already highly charged between the two title protagonists prior to the explosive British GP.
"The relationship will certainly become even more tense now," Marko told RTL. "Let's put it this way - it was never a relaxed relationship.
"But that's exciting for the audience," said the Austrian. "We will behave within the fair, sporting methods.
"We know we have a great package. This is a major setback, no question about it, and we think it is a very unjust one. But we're strong enough to take it.
"We won the sprint at Silverstone with ease, and we would have won the main race too - that was very clear. We have proven that we are competitive on every race track this year.
"Budapest will be similar, although it has completely different track characteristics. It has always been dominated by Mercedes but that is no reason for us to be afraid.
"We assume that it will be very close again, but hopefully the duel will take place on a fair level. Then we are very optimistic that we will win again."
However, whilst declaring Hamilton's 10-second penalty as "ridiculous", Marko admitted: "Maybe the regulations are to blame. They are quite restricted.
"We should probably revise the code, including the stewards system. Perez got 5 seconds for marginal contact without anything flying off the track, and they could have made Hamilton drive through the pits too. But they didn't."
Former F1 driver and British commentator Martin Brundle, however, says Red Bull can only challenge Hamilton's penalty if "new evidence" comes to light.
"I am told by Red Bull that there is data to prove Lewis was significantly faster into Copse than at any other time and he would not have made the corner without running wide and inevitably contacting Max," he told Sky.
"Presumably, that will be made publicly available, and if Red Bull feel they have new evidence they may well make an appeal to the FIA as to their perceived degree of fault and leniency regarding Hamilton."
