The Mercedes driver initially suspected it was a car failure but later admitted it was his mistake to the stewards.
The stewards took no action on a separate incident between Jenson Button and Sebastian Vettel.
Button 'closed eyes' in Vettel incident
Schumacher lost his Mercedes under braking following the first safety car period and hit the Toro Rosso driver, forcing both cars out of the race.
A stewards' statement said: "The driver acknowledged that the collision was his error due to failure to anticipate braking performance of the car with lower tyre grip following a safety car period."
Before speaking to the stewards, the seven-time world champion said: "I just went straight on the brakes very hard, locked up everything and tried to brake as hard as possible but the accident wasn't avoidable any more."
Button admitted to closing his eyes when leader Vettel braked suddenly under the safety car.
The McLaren driver was caught out, locking his brakes and only narrowly missing out on making contact with the leading Red Bull.
Vettel reacts to Singapore success
But the stewards said: "An examination of the telemetry overlay for throttle, steering and brake traces of both cars did not indicate any erratic driving behaviour on the part of the race leader.
"It is noted that article 40.13 [of the sporting regulations] provides that the first car may dictate the pace."
Speaking before the incident, Red Bull boss Christian Horner said: "The leader dictates the pace so I was concerned Jenson nearly drove up the back of him. It just looked like Jenson mis-judged it completely."
McLaren team boss Martin Whitmarsh said: "He [Sebastian] weaved, accelerated, and once you go, you go. You don't then hit the brakes halfway through the corner.
"They were both quite lucky and could have gifted Fernando even more points."
Button added: "Sebastian accelerated and braked for the right-hander and I just didn't expect such a speed difference, so I hit the brakes, locked up and just missed the rear of his car. That would have been quite embarrassing."
Singapore Grand Prix 2012, day three
Sunday, 23 September: Highlights on BBC Three at 19:00 BST.
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