The social media giant said 'no' to immediately handing over evidence that may be on suspect Stephen Nicholson's Facebook account.
But headteacher Jason Ashley told a special assembly he was 'desperate' for Lucy's friends to provide information to help crack the case.
"She can't fight for herself any more – we can, we can do that for her," he said.
"If you need help, if you've got information, we are desperate to help you. There's a bit of me that thinks someone in our school community may know something."
The headmaster's rallying cry came after Britain's most senior police officer said police should have access to suspect's Facebook accounts "within minutes".
Prime suspect Stephen Nicholson refused to give his Facebook password to officers quizzing him over the murder of Lucy McHugh, 13, in Southampton.
Nicholson, 24, got 14 months’ jail for not surrendering his private messages.
Scotland Yard chief Cressida Dick said cops are often blocked from getting vital evidence or forced to go through “a protracted procedure” to obtain information from social media companies.
She told LBC presenter Nick Ferrari: "I absolutely think that in certain instances, and it sounds to me like this is one, law enforcement in the UK ought to be able to have vital evidence which might bring somebody to justice."
Lucy McHugh was stabbed to death six weeks ago and her body dumped in woodland in Southampton.
Nicholson, a father of one, was staying at Lucy's family home until several days before she was found on July 26.
According to prosecutors, he had contact with the teenager as recently as the morning of her disappearance.
While being questioned on suspicion of murder and sexual activity with a child, he twice refused to give detectives his Facebook password.
Lucy's mum Stacey White said Facebook has turned her daughter’s private account into a public memorial page without permission.
She told the Daily Mail: "They should give over the account details. Lucy needs justice. It's so easy for them to do."
Investigators face having to take lengthy legal action in the US in order to obtain access, with the delay branded "deeply disturbing" by the head of the Commons Home Affairs Select Committee.
Yvette Cooper, chairwoman of the Home Affairs Select Committee, called on the Government and Facebook to create a fast legal procedure for such cases.
"This was an appalling murder, and Lucy McHugh's family need justice," she told the Mail.
"For there to be such long delays and cumbersome international processes for getting crucial information in such a serious case is deeply disturbing."
Facebook told the paper it was "co-operating with Hampshire Police".
Nicholson remains on bail for his arrest on suspicion of murder and sexual activity with a child.
A charging decision is anticipated on October 27.
A Facebook spokeswoman said: "This is a terrible case and our hearts go out to the family of Lucy McHugh.
"We are working closely with law enforcement and there are well-established legal mechanisms that the police follow to obtain information in criminal investigations like this."
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