The British driver and his team mate Takuma Sato were conspicuous by their absence at a Spanish Grand Prix that his Honda-powered team had hoped to win before being banned for two races on Thursday.
BAR were punished for a breach of the rules with their car's weight and fuel tank at last month's San Marino Grand Prix.
Their trucks pulled out of the paddock on Friday, not to return until the European Grand Prix at the Nuerburgring in Germany on May 29 after the glamour highlight of the championship in Monaco on May 22.
Button, who intended to watch the race on television, will have taken little comfort from seeing McLaren's Kimi Raikkonen winning ahead of Renault's Fernando Alonso.
"I never want to be a test driver. It's the most boring thing, sat around watching cars go around," he had told reporters on Friday.
"I'm sure I can find some way of looking after myself over the Monaco Grand Prix," he added. "But that will be the tough one, being there and not going out because it is such a spectacular event. It's one of my home grands prix.
"Waking up in my apartment and hearing the cars go round is going to be a bit weird."
CONSIDERABLE RESPECT
While speculation was rife, with various theories about the BAR affair, most rivals preferred not to comment on an episode that did not cast Formula One in the best light.
"They are a very proficient racing team and we still have considerable respect for them. When they come back after their two-race ban, they are going to be very strong," said McLaren boss Ron Dennis.
Ferrari boss Jean Todt wondered whether Michael Schumacher might have won at Imola had Button not kept the seven-times champion behind him for as long as he did.
"Maybe we lost the race in Imola because of that, because if you see how many laps Michael spent...but that is history," added the Frenchman.
Red Bull collected a point for eighth place with David Coulthard in Barcelona but team boss Christian Horner said it was not necessarily thanks to BAR's absence.
"It depends which BAR you are talking about," said Horner, asked whether they had benefited from the ban. "If it was a Melbourne BAR no. If it was the Imola one, then yes."
"But BAR are a very strong team and it's important for us to capitalise and take as many points as we can while they are not here," he added.
Button promised BAR would be back strongly.
"As soon as we get to Nuerburgring, they will realise that it's not down to what people think," he said. "We are a very good team and we have a lot of exceptional people working here and we will prove that when we get to Nuerburgring.
"I wouldn't say it's going to be revenge but it'll be great getting to Nuerburgring after the races off and show that we are very strong and that our pace is down to everyone involved in the team."
