BAR will not fight motorsport's world governing body over their two-race ban, say the team's co-owners Honda.
Jenson Button came in third at Imola
The FIA ban followed the discovery that Jenson Button's car was underweight after the San Marino Grand Prix.
"We felt the punishment was too harsh but any appeal now would only be bad for the sport," said Honda spokesman Tatsuya Iida on Tuesday.
"We had just got the car to perform to expectations so the timing of the ban is a big blow. It's very sad."
BAR had earlier vowed to fight the decision of the FIA's International Court of Appeal before opting to criticise the severity of the punishment instead.
The FIA then claimed on Monday to be looking at BAR's comments to see if they can be charged with disrepute.
"Statements attributed to the management of BAR-Honda are currently under investigation in the light of the team's obligation to do nothing 'prejudicial to the image and dignity of F1 racing' or 'prejudicial to the interests of any competition or to the interests of motor sport generally'," said a FIA statement.
The FIA have also batted off criticism of their appeals court, which five of the Formula One engine manufacturers want replaced by the independent Court of Arbitration for Sport.
The statement added: "The manufacturers concerned came into Formula One for their own reasons.
"They were not invited - they invited themselves. Each of them accepted the rules and structures of the sport as they had done on many previous occasions."
The FIA issued the statement after BMW, DaimlerChrysler, Renault, Toyota and Honda, which owns 45% of BAR, had called for an "independent appeals process administered by an internationally recognised body" to settle disputes.
Officials apparently took that as a slight on the integrity of the appeal court.
The five companies, who represent the Williams, McLaren, Renault, Toyota and BAR teams, have been at odds with the FIA over a number of issues.
And they have threatened to set up a breakaway series in 2008 if they are not granted a greater say in how Formula One is run.
The bitterness intensified in January when Ferrari signed a deal with commercial rights holder Bernie Ecclestone and the FIA committing to F1 until 2012.
Although the rebel manufacturers intend to lobby the FIA on the appeals issue, they have agreed to stick with another controversial proposal.
FIA president Max Mosley demanded a cut in engine capacity for next season to 2.4 litres, and the five carmakers indicated that shoud remain in place post-2007 "to ensure stability for engines for three years".
"Beyond 2008, the manufacturers will jointly develop a new engine proposal for the sport," the statement said.
Two recent meetings with Mosley were shunned by the rebel manufacturers and their teams, but they appear to have softened their stance.
"The manufacturers look forward to meeting with the FIA in the near future to discuss this and other matters concerning regulations post 2007 and will continue to work in conjunction with the nine teams," the statement added.