Tom Rodwell, 31, from Middlesbrough, had previously admitted 10 rapes, one attempted rape and a sexual assault.
In January, he was sentenced to life in prison with a minimum term of 12 years.
A request for his punishment to be reviewed under the Unduly Lenient Sentence Scheme was refused as it did not meet the criteria.
The Attorney General’s office said a referral could only be made to the Court of Appeal “if a sentence is not just lenient but unduly so”.
A spokesperson said the sentencing judge would need to have “made a gross error or imposed a sentence outside the range of sentences reasonably available” in the circumstances.
“The threshold is a high one, and the test was not met in this case,” they said.
Teesside Crown Court heard Rodwell raped five women on multiple occasions between 2017 and 2020.
The jury was told the former Royal Navy and HMRC employee “did not realise or seem to care that he needed consent” and he told one victim he wanted to “own her” and “choke her”.
Judge Paul Watson described Rodwell as a “callous, unfeeling sexual predator” and a “significant danger” to women.
The victims, some of whom were university students, were not just physically abused but also manipulated emotionally, leaving some to believe they were to blame.
During the hearing it emerged that Rodwell, who had no previous convictions, faced similar charges in Scotland in 2018 but was acquitted.
