The teenager, who cannot be named for legal reasons and was referred to as 'C', is from the London Borough of Brent but went to school in nearby Barnet, London's Civil Appeal Court heard.
The London Borough of Brent has a policy that any child expelled from school is required to attend a pupil referral unit (PRU) in the aftermath of exclusion.
However she attended the centre only once before refusing to go back - finding it 'frightening and intimidating', her counsel, Ian Wise, told the Appeal Court.
Lady Justice Smith, sitting with Lord Justice Laws and the Master of the Rolls, Sir Anthony Clarke, refused to overturn an earlier High Court ruling in the council's favour.
She said Brent had fulfilled its legal obligations to the girl, but she also noted that the council had not communicated closely enough with C's parents.
The judge said the girl, who had received 'glowing' reports, had been 'severely bullied' during her time at school in Barnet. Teachers had described her as a 'pleasure to teach'.
Lawyers for the girl had claimed that the council had 'failed to provide her with suitable education' as required under the Education Act.
They claimed that the High Court judge who earlier dismissed C's judicial review challenge had 'erred in failing to have proper regard to the practical impediment of C attending the PRU'.
However, dismissing the appeal, Lady Justice Smith said the council had carried out its Education Act duties by offering C a place at the PRU.
But she added: 'However, we have considerable sympathy with the view of C and her parents. The council has never explained why it feels it can protect C at the PRU.
'If the council had recognised the sincerity of the family's concerns, and had been prepared to meet them for discussion, it is likely that this impasse would have been avoided.'