In another dramatic twist to the saga surrounding F1's qualifying system, sources have confirmed that the two outfits were unwilling to play ball with an alternative solution that had been put on the table by the FIA this week.
And without their support - and the need for unanimous backing for any change to go through - the idea to tweak elimination qualifying was left dead in the water, with no time left to do anything other than keep the system that proved so unpopular in Australia.
After the shambolic end to Q3 in Australia, teams had unanimously agreed in Melbourne to ditch elimination qualifying and go back to last year's system for the next race in Bahrain.
However, a decision was made by the FIA to not go that far and abandon the positive aspects of the change. Instead it wanted to give the shoot-out system another try, albeit in an improved format.
This week therefore, teams on the Strategy Group and F1 Commission found themselves only able to vote on a revised format to elimination qualifying proposed by the FIA, where the new-style Q1 and Q2 would be extended, and Q3 would revert to how it was last year.
One theory as to why teams were only given this option to vote on was that it would effectively force their hands to accept it, as they would be highly unlikely to reject it and keep the Australian system that was so universally criticised.
However, if that was a motivation for not giving teams the option of going back to last year's system, then it failed entirely because McLaren and Red Bull refused to support it and did not vote in favour.
Without their support, the vote did not go through, meaning that F1 is heading to Bahrain with the same under-fire elimination qualifying format that was run in Australia – and little prospect of it delivering a better show in Q3 this time.
In a week when the GPDA spoke out about F1's 'obsolete' rules structure, and the sport making a bold move away from free-to-air TV in Britain, the inability of F1 to get rid of a hated qualifying format has left it facing further criticism.
F1 chiefs will almost certainly get together after the Bahrain Grand Prix to decide what to do for the remainder of the season - and it appears likely that teams will only accept going back to last year's format in its entirety.
Red Bull boss Christian Horner said in Australia that the month-long saga surrounding elimination qualifying has not been good for F1.
"I don't think we probably handled the whole qualifying thing that well," he said. "I don't think we covered ourselves in glory with it.
"But the important thing is to learn from it. Any change has to be fully considered about what the consequences are, and I don't think we did that.
"The intentions were there, for all the right reasons, it just didn't achieve what was intended. The teams shouldn't run the sport. That's the fundamental thing."
This story by Jonathan Noble originally appeared on Motorsport.com, the world's leader in auto racing news, photos, and video.