A panel of judges headed by the Lord Chief Justice Lord Thomas rejected the application on behalf of the 16-year-old, who stabbed Mrs Maguire, 61, seven times from behind as she taught a Spanish class at Corpus Christi Catholic College in Leeds in April last year.
The appeal related to the least time Cornick must spend in custody before he is eligible to apply for parole.
Whilst passing his sentence back in November, Mr Justice Coulson warned Cornick, who was 15 at the time, that he might never be released from prison as he passed sentence at Leeds Crown Court.