In 2016, the Sendai district court ruled two local governments should pay a combined 1.43 billion yen ($13.7 million) to 29 plaintiffs -- parents of 23 children who were killed in the disaster.
The victims, from the public Okawa Elementary School in the city of Ishinomaki, were among a total of 74 children who perished in rising waters after being told to wait for more than 40 minutes in school grounds with teachers, 10 of whom also died.
The plaintiffs argued their children would have survived if they had been evacuated in time.
The local governments appealed the 2016 decision, but on Thursday the Sendai High Court said the lower court ruling was correct, local media reported.
"(The school) should have been able to forecast before the occurrence of the quake that a tsunami would reach the school," broadcaster NHK quoted presiding judge Hiroshi Ogawa as saying.
"The school had an obligation to clarify evacuation areas and evacuation routes in its risk management manual but it failed to do so," he added.
Kyodo news agency said the court increased the compensation awarded in the earlier decision by around 10 million yen.
The original sum was around 1.4 billion yen ($13 million).
Hiroyuki Konno, who lost a 12-year-old son and spoke on behalf of the plaintiffs, told NHK he was "thankful that cooperation and support from many people have led to today's ruling".
"I think the fact that organisational responsibility was acknowledged will be useful for future disaster prevention."
"I'm relieved," added another parent, Kazutaka Sato, speaking to NHK.
"The trial was long and there were times I wanted to run away. But we were able to bring our voices to the public thanks to support from many people."
A massive undersea quake on March 11, 2011, sent a giant tsunami barrelling into Japan's northeastern coast, leaving more than 18,500 people dead or missing, and sending three reactors into meltdown at the Fukushima nuclear plant.
It was Japan's worst postwar disaster and the most serious nuclear accident since Chernobyl in 1986.
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