"We're going home now, the guys are packing up, everyone understands the situation," said team boss Nick Fry at the Spanish Grand Prix.
The team, backed by British American Tobacco and Honda, will now miss Sunday's race in Barcelona and the glamour highlight of the season in Monaco on May 22.
"Upon receiving the best legal advice, in all relevant jurisdictions, the conclusion is that nothing can be done to enable the team to race this weekend," BAR said in a statement.
"BAR Honda has considered whether to pursue further action which might enable it to compete at Monaco.
"On balance, the team has decided that to challenge the sport's governing body (the FIA) would cause a level of disruption and damage to the sport which would not serve the best interests of everyone involved."
Fry said the team had explored every legal avenue and deliberated until after midnight to try and prevent a hugely costly exclusion.
"I haven't sat down and calculated what it is at the moment but in terms of contractual obligations that we'll have to meet I could confidently say this is going to add up to more than 10 million (dollars) I would imagine," he said.
BUTTON'S FUTURE
BAR have also been stripped of their points from last month's San Marino Grand Prix. Briton Jenson Button had finished third while Japanese team mate Takuma Sato was fifth.
Those points were BAR's first of the year and the team will be seven races into the season before they can open their tally.
That could threaten their hopes of retaining Button next season after a contract war with Williams last year.
"We've made things more difficult for ourselves, no doubt," said Fry. "But we want Jenson for 2006 and beyond."
Both drivers turned up on Friday, ready to take part in practice should the team give them the nod. It never came.
"I think this has gone as far as it should go now, we've made our point very strongly," said Fry.
"We remain insistent that we've done nothing wrong, we still think that the penalty is excessive but the lawyers are telling us that the issue of jurisdiction is a very difficult one.
"We can't find a court that is willing to say 'yes, it's our responsibility'. The case seems very sound, the only possibility looked like it would be in France (where the FIA are based) but that can't be done in time."
A motor racing appeal court, dealing with a complaint by the sport's ruling body against its own stewards, ruled on Thursday that the only way the BAR car could have achieved minimum weight requirements in Imola was by using fuel as a ballast which was against regulations.
The court's finding on Thursday spoke of a "special compartment within the fuel tank". Its contents allowed the car to reach minimum weight requirements.
Fry said he believed other teams were no different.
"We know that the other teams have got similar systems," he said. "The fuel tank supplier who supplies us is the same as many of the other teams, they confirm there is nothing unusual about our system.
"There have been rumours that other people are looking at their cars overall. This is a very draconian interpretation of the rules and I think its made everyone look carefully at what they are doing."
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