BAR have admitted they now face a battle to keep Jenson Button following the team's two-race ban.
The British driver can leave at the end of the season if BAR fail to fulfil the performance clauses in his contract.
The team will arrive at their next race in Germany with no points and chief executive Nick Fry admitted: "We have made it more difficult for ourselves.
"But there are lots of races to win. We have certainly not given up. We want Jenson for 2006 and beyond."
BAR were punished for breaking weight restrictions at Imola last month, leaving Button and team-mate Takuma Sato to sit out the Spanish and Monaco Grands Prix.
Button, who tried to leave for Williams last season, has given up on winning the drivers' title but insists the ban has not made him want to walk away from BAR.
"You've got to say that our chance of winning the championship is pretty much gone," he said.
"To come back's pretty much impossible, especially with Renault being so strong in the first few races and Ferrari will be strong for the rest of the year.
"This is difficult for everyone involved, but it's not something that makes you want to walk away from the team, no way.
"I completely trust everyone involved. I have got confidence in everyone in the team here, in the technical staff and the engineers, that we are legit and we will always race to what we think is in the rules."
Button had arrived in Barcelona in confident mood after setting an unofficial lap record on the track in testing last month, and clocking some good times in testing at Mugello.
"With the step we made at Mugello I thought 'wow we are going to have an awesome year this year'. This is the first one I thought I had a chance to challenge for the championship," he said.
"I'd worked it out I had to beat [championship leader] Fernando Alonso by two points in every race, which I thought was reasonable."
Button's ban means he will not return to action until the European Grand Prix on 29 May.
"There will be a lot of people in the team upset with the decision but we will come back strongly at the Nurburgring and give everyone something to think about," said Button.
"I think we will be very strong and very determined to show we are a strong team that can fight for wins, not just podiums.
"There's no use getting all hyped up about what's happened. We have to just get our heads down so when we get to Nurburgring we just destroy everyone."