"Facebook is a real nightmare for schools and this incident is particularly unpleasant," he said.
"We have a lot of concerned parents and pupils who do not recognise the school in this. We are dealing with it very robustly and have reported it to the police, but the situation is extremely frustrating.
"All schools are doing a lot of work to make sure students use IT responsibly and to make sure they are aware of the risks and we will be stepping up our efforts in that area, but it's the lack of our ability to close down such sites quickly that is so frustrating for schools."
A spokesman for North Yorkshire Police said: "We are looking into reports of offensive comments being made by school children on a Facebook page.
"The school has been given advice about having the page removed by Facebook."
He added parents, young people and carers could report online abuse using a Child Exploitation and Online Protection Centre (CEOP) application on Facebook.
A spokesman for Facebook said: "The page has been removed as it broke Facebook's terms as set out in our statement of rights and responsibilities.
"Whilst we don' t comment on individual cases, content can be removed for a number of reasons such as bullying or harassing another user. We encourage people to use the tools available on every page of our site to report content to us."