Judges at the Court of Appeal Edinburgh rejected Stephen Murray's challenge and ordered him to serve an extra two-and- a-half years in prison – a move welcomed by politicians and charities.
Murray, from Larkhall, in Lanarkshire, admitted raping a 65-year-old woman and indecently assaulting two other dementia patients, aged 84 and 74, at the South Lanarkshire care home where he worked between December 2010 and April last year.
Sentencing, Lord Turnbull said the 44-year-old deserved a sentence of nine years, but reduced it to seven in light of his early guilty plea.
Murray went to the appeal court claiming he should have received a greater discount, but Scotland's senior judge, the Lord Justice General, Lord Gill, rejected his claim, stating the appeal was "ill-advised".
In a written judgment on the case, Lord Gill said: "In my opinion, the figure of nine years is unduly lenient.
"The crimes to which the appellant pled guilty were vile. They involved a grievous abuse of trust.
"The appellant committed these offences against helpless women whom it was his duty to treat caringly and respectfully.
"His conduct is aggravated by the fact that, on his own admission, he chose his victims because they were incapable of any meaningful communication with others. The consequences of these crimes on others should not be underestimated."
The Lord Justice General said he considered the starting sentence should have been 12 years, which would be reduced to nine-and-a-half years following the guilty plea.
Alzheimer Scotland said the sentence increase sent a clear message that abuse of this kind would be treated "with the severity and greatest weight the courts can lend to it".
Its chief executive, Henry Simmons, said: "We have been appalled by this man's actions and are very pleased the appeal judges have decided to increase this sentence.
"Any individual who abuses their position and exploits a person with dementia when they are at their most vulnerable deserves nothing less than the full force of the law to fall upon them.
Local MSP Christina McKelvie added: "A lot of people were unhappy with the original sentence, including myself, so I would welcome this increase – it's a good day for justice.
"Stephen Murray took advantage of vulnerable people who had put their trust in him."
Staff at the care home also welcomed the decision. The unit's director of nursing said: "We absolutely welcome the increase in sentence. I personally still don't think it's enough, but I'm sure I speak on behalf of all the staff when I say any increase is welcome.
"This lady's family have had a horrendous time – they've been put through hell."
Murray was found by a colleague with one of the residents he assaulted. He later said: "I'm so ashamed. People will think I am a pervert."
Police were called, but before they arrived he cut his neck with scissors in an apparent suicide attempt.
He later admitted raping one dementia sufferer in April and abusing the other two.
At the time of the sentencing, the families of the victims were described as being shocked, disgusted and devastated by the offences.
Lord Gill added that the appeal was misconceived as it was based on an idea that an early guilty plea entitled every accused to a one-third reduction in sentence – a claim he considered had been clearly discredited in a previous appeal court decision.
He said that as there was no question of any of the victims having to give evidence, the value of Murray's plea – which prevented a trial – was greatly reduced.