With Massa and Bottas squabbling over seventh and eighth places in the closing laps, the Brazilian was instructed over the radio that his team-mate was much quicker and to let the Finn by to allow him a crack at sixth-placed Jenson Button.
Massa, humiliated in the 2010 German Grand Prix when given the same instruction from the Ferrari pitwall at a time when he was leading the race ahead of then team-mate Fernando Alonso, refused to yield.
Massa insisted after the race he was right to hold his station on this occasion, and the team were wrong to issue such an order.
Following international discussions over the past few days within the Grove-based marque, deputy team principal Claire Williams claims the matter has now been resolved, with humble apologies all round.
"At Williams we want our drivers to race, we always have, and we're a team that's renowned for that, not a team that has a number one and a number two driver," said Williams.
"What happened is we weren't necessarily prepared for the scenario that actually arose on the day.
"Certainly the instruction given in the way it was given, considering history (with regard to Massa), wasn't the most advised.
"For us as a team we're disappointed in ourselves because what was said over the radio we wouldn't want to be heard by everybody.
"Our fans expect us as a team to let our drivers race, and that's the over-riding disappointment.
"So to our fans we want to apologise because we didn't handle it in the best way, and to let them down is not the way we want to go.
"Of course, we've apologised to our drivers, which was the right thing to do at the end of the day."
Massa and Bottas are both confident what the former has described as "a mistake" will not be repeated in future, and the team harmony has not been fractured.
"I don't think it has damaged my relationship," said Massa, who moved to Williams from Ferrari over the winter.
"When I do something that is my mistake I will be the first to say sorry, and in this case the team were the first to say sorry as well.
"Everything is now agreed inside the team and I have no problems working for the team when it's necessary and at the correct time.
"If it does happens again when it is not correct, I don't know what will happen."
As for Bottas, he said: "We've sat down with the team and talked it through, and we've clear rules for the future.
"As a team there are some things we could have done better, but we will learn from it, and hopefully we will be allowed to race a bit more."