Two-time defending champion Hamilton was leading an incident-packed race and looked set to reclaim the championship lead from Rosberg when he was forced out on lap 41 of 56 in Sepang.
It was the latest in a series of engine and technical issues that have hindered the Briton's bid for a third straight championship and Hamilton was implicit in his criticism of his previously all-conquering team.
"My questions are to Mercedes -- we have lost so many engines -- someone has to give me some answers, it is not acceptable," he told BBC Sport.
"Something or someone doesn't want me to win this year," he added.
With Hamilton sidelined, Australia's Daniel Ricciardo took his first win of the season ahead of 19-year-old Max Verstappen, who drove another superb race to bely his tender years.
Rosberg, fighting his way back through the field after being taken out on the first corner as Ferrari's Sebastien Vettel span out, eventually claimed a battling third place.
Vettel was later handed a three-place grid penalty for his part in the incident.
The German, who had been given a 10-second penalty for an overtaking move on Kimi Raikkonen, managed to open up a bigger gap over the Ferrari man by the finish to gain an extra three points, which could prove crucial in the title race.
With only five rounds to go, Hamilton has a mountain to climb to overhaul his teammate and Mercedes non-executive chairman Niki Lauda attempted to cool the public row.
"We should not let him down with an engine failure, it was a fairly new engine, it was not old in the car. What went wrong I do not know and we will work to correct it," Lauda told Sky Sports.
"I'm taking him to Japan tomorrow in my plane., I hope I can bring him up. The championship is over when the last are is over, 23 points is a lot but you never know.
"We have done nothing against him. We have people working for him, we are proud of him and these things happen," added the former F1 legend.
Next weekend's Japanese GP at Suzuka will give Hamilton an early chance to claw back some points, but Mercedes faces a renewed challenge from Red Bull, which has pulled clear of Ferrari in the battle for second place in the constructors' title with its maximum in Kuala Lumpur.
For Ricciardo it was deserved consolation for earlier near misses this season in Monaco and the previous round in Singapore, where he pushed Rosberg all the way.
It was his first win since 2014 and has cemented his third place in the title race behind the Mercedes pair.
"It has been two years since the last win and it's been a bit emotional," he said at the podium presentation.
"We have come close but I said two weeks ago we would win one and we did."
Rosberg, bidding for his first world title, could not believe his luck after being caught up in the first corner incident as Vettel and Verstappen tangled in a battle for position.
"I thought the race was all over, so I am really happy to fight back all the way to the podium," he said
Behind the leading contenders, Valtteri Bottas drove a fine race in his Williams for fifth, ahead of Sergio Perez of Force India.
There was another seventh for Fernando Alonso in the McLaren, with his teammate Jenson Button in ninth in his 300th Grand Prix.
Britain's Jolyon Palmer claimed his first point of the season for Renault in 10th place.