A lawyer for Llewelyn James said a trial judge in 2007 was wrong to let prosecutors use statements James made after he was arrested in February 2002.
The three-judge panel on Friday ruled a statement made to a cousin was properly admitted and it was OK for detectives to question James because an uncle gave his consent.
The court also says consecutive sentences were appropriate because each killing was a separate crime.
James' sentence is one of the longest ever in New Jersey.
James was 16 when he killed his aunt and four others in Winslow Township, then two others in nearby Lindenwold days later.