Mitchell's lawyers had claimed that the interview was conducted in circumstances which were wholly and manifestly unfair to the teenager.
"Having considered the transcript of the interview, we are driven to the conclusion that some of the questions put by the interviewing police officer can only be described as outrageous," Lord Hamilton said.
"At times, the nature of the questioning was such that the questioner did not seem to be seriously interested in a response from the appellant but rather endeavouring to break him down into giving some hoped-for confession by his overbearing and hostile interrogation.
"Such conduct, particularly where the interviewee was a 15-year-old youth, can only be deplored."
A police spokeswoman said: "We duly note the comments made by the appeal judges.
"We will talk time to consider the statements; it would be inappropriate to comment further.
"This was a grave crime and our thoughts are with the family at this time."
Jodi was stripped, tied up and stabbed to death in woods near her Dalkeith home. The judge at Mitchell's trial described it as the worst murder case he had ever seen.
Mitchell, who has always protested his innocence, was found guilty after the longest single-accused murder trial in Scottish legal history.
During the 10-day appeal against his conviction and sentence, Mitchell's lawyer Donald Findlay QC claimed his client did not receive a fair trial because of the imagery of newspaper headlines which would have been read by jurors before the case came to court.
Mr Findlay also claimed there was insufficient evidence presented to the jury to allow them to find Mitchell guilty beyond reasonable doubt.
BBC Scotland cameras were in court to film the proceedings.
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