In an open letter on their website addressed to fans, the team also outlined how Nico Rosberg's lead was also jeopardised by 'alarming' read-outs from the MGU-K, which forced the German to complete the race in a 'safe' mode. Mercedes conceded that both incidents highlighted how they have 'not met your own expectations' in terms of reliability in 2016.
"We were baffled and gutted by the repeat MGU-H failure on Lewis' car in qualifying," Mercedes explained in reference to the Briton's issues on Saturday, "but we kept calm, gathered our thoughts and sprung into action.
"It took a monumental effort from a significant number of people back in the UK and in Russia to fly spare parts out to the track, fit them to the spare Power Unit by working through the night and make sure Lewis could start from P10 on Sunday without having broken parc ferme.
"[In the Grand Prix] we started to see the water pressure falling on Lewis' car. At the time, he was pushing hard to catch Nico and pull away from Kimi - posting several purple lap times in the process.
"We needed to await confirmation from the FIA of what we could tell him via the radio. After several calls asking him to take it easy, the all-clear came to let him know that he was losing water pressure.
"With zero - yes, zero! - water pressure remaining for the last 16 laps, the job he did to nurse the car home and still retain second place was truly remarkable. He had to keep the car as cool as possible to avoid damaging the engine whilst also keeping Kimi at a safe distance, which was no mean feat.
"We genuinely aren't sure by what miracle the car limped across the line - but we're certainly not going to complain."
As for Rosberg's problems, Mercedes added: "Shortly after his pit stop, we saw some alarming behaviour from Nico's MGU-K.
"We spent a number of laps reassuring him that he had a good gap over Lewis and could ease off before the FIA gave us the all-clear to tell him to switch to a setting that would control the issue.
"At the wheel, Nico wouldn't have had any inkling of the stress on the pit-wall. When he put in the fastest lap on the penultimate lap of the race, he was still in that 'safe' setting – demonstrating just how much pace the car had last weekend."
Mercedes said that they were therefore extremely grateful just to get both cars home, but stressed that the dominant nature of their one-two in Sochi will not lessen their desire to keep improving.
"Ultimately, none of this changes the fact that we have not met our own expectations in terms of reliability so far this season," their letter continued.
"Performance-wise we are right on the money - with a points haul just two shy of what we had managed by the same stage in 2015. But there is work to be done.
"From what we've seen so far, [the 2016 season is] going to be one heck of a rollercoaster. There will be highs and lows, good day and bad days, successes and defeats.
"But, through all of this, we stand united as a team - just as we always have. To those who stand with us, we thank you. And to the rest - the haters, the naysayers, the conspirators... if we can convince even half of you of what we really stand for, we'll consider that a battle well won."