The publishers of 'Daily Mirror' and 'Sunday Mirror' had argued that the 1.25 million pound it was ordered to pay in total to victims was "out of all proportion" to the harm done to them.
In May, Justice Mann awarded compensation to eight people including Indian-origin actress Shobna Gulati and former footballer Paul Gascoigne.
He said the invasions of privacy were "serious" and "prolonged".
The Mirror Group agreed it would pay but had disputed the amounts.
Lady Justice Arden, Lady Justice Rafferty and Lord Justice Kitchin upheld Justice Mann's judgement.
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"MGN cannot expect this court to come to its rescue and find some way of finding the awards to be excessive when its staff have been responsible for disgraceful conduct with such distressing consequences, and when to boot it is quite unable itself to point to actual awards that it contends are wrong," Arden added.
With the publisher facing further phone-hacking claims from more than 100 alleged victims, the failure of its appeal means it could now be facing more large payouts.
The UK ended its four-year-old probe into the mammoth scandal that rocked country and led to the tabloid's closure on December 11.