A team statement said BAR had decided not to take further legal action to avoid damaging the sport.
BAR has accepted this will mean the team will be unable to race at the Spanish Grand Prix this weekend and in Monaco on May 22.
The statement read: "On balance, the team has decided that to challenge the sport's governing body would cause a level of disruption and damage to the sport which would not serve the best interests of everyone involved."
The team says the two-race ban will cost them millions of pounds. It added that missing Monaco would trigger penalty clauses in their sponsorship contracts.
BAR results have been cancelled from the last race in San Marino, leaving both their drivers with zero points in this year's championship.
The ruling, which also included disqualification from the Imola race and a six-month ban suspended for a year, was the toughest sanction taken against an F1 team for 20 years.
The team says it will discuss the ramifications of the decision with their fellow teams and engine manufacturers.
BAR’s statement adds: “The FIA International Court of Appeal in its own judgement was unable to prove that the team acted in bad faith. BAR Honda therefore remains unclear as to the basis for such a severe penalty.”
