Ross Brawn and Martin Whitmarsh have criticised British politicians for their belated stance on the Bahrain Grand Prix.
Labour leader Ed Milliband on Friday called for Sunday's race to be cancelled, citing "violence...and given the human rights abuses".
Milliband then called on the Government to "make its view clear and say the same", however, Prime Minister David Cameron refused to do so, claiming it was "a matter for Formula One".
Cameron added there is "a process of reform under way in Bahrain" which his Government supports and wants to help promote.
Milliband's position followed 17 MPs signing a cross-party motion at Westminster calling for the race to be called off.
They suggested it would be used by the Bahrain government as "an endorsement of its policies of suppression of dissent".
Brawn, however, feels the MPs' reaction has effectively been a case of closing the stable door after the horse has bolted.
"We're here now, and after this event we need to sit down and discuss it," said Brawn.
"We were committed to this race and after the race we will make a proper judgement of what happened and come to a conclusion.
"But I find it very frustrating that politicians in the UK were saying we should withdraw once we got here. Why didn't they say anything beforehand?"
Labour MP Yvette Cooper went one step further by suggesting all three British drivers in McLaren's Lewis Hamilton and Jenson Button, as well as Force India's Paul di Resta, should withdraw.
Brawn added: "For somebody to try and make Jenson Button or Lewis Hamilton determine the foreign policy of the country is wrong."
Whitmarsh concurred as he said: "I don't think it's helpful to wake up this morning and hear we shouldn't be here when we are already here, so I endorse what Ross says."
