Unfortunately if your letter of refusal does not state you have a right to appeal then it is unlikely that you do. You will need to provide additional information in a written letter to the address stated in the letter you received. You should also include any supporting documents. You would normally have a right to appeal if you raised humans rights grounds.
You asked in your question "how do you suggest me to inform the Home Office" I gave you an answer which is to inform the Home Office by way of a letter. You did not disclose the fact that the letter asks you to make a new application.
In order to give the best answers to questions experts on JA rely of users disclosing all relevant information and not by piecemeal.
I have not had sight of this letter you received neither was I aware of the full content of it but it sounds like you have received a RED0001 notice within a caseworker decision letter which simply is a refusal decision with notice that you are a person liable to be removed from the UK. The letter would ask you to give any additional grounds upon which you should not be removed from the UK otherwise you may make a further application to regularise your status in the UK. If this is the case you should be seeking independent immigration advice. Experts on JA are not allowed to give advice particularly in this type of situation.
So if you have any grounds why you should remain in the UK, you should state those grounds in a letter to the Home Office but if you are eligible to apply under a different visa option then you should be making that application before the deadline. You may also choose to make a new application under FLR(O) as you did before with any additional grounds informing the Home Office why they should grant you a visa. In any event you should seek independent legal advice.