No.
The services provided by you are covered under Rule 3 of the Place of Provision of Services Rules, 2012. Meaning, the place of provision of for your services would be based on the location of service recipient.
Please note that if the place of provision is outside India, no service tax is payable on such services.
Therefore, in your case, you would not be liable to service tax, even if you don’t receive the amount in foreign currency.
Further, you must also note that if you don’t receive the amount in foreign currency then you will be denied to claim Cenvat credit for claiming refund. Therefore, for claiming refund, you must receive the amount in foreign currency.
As you stated the amount has been received in foreign currency, you satisfy the condition, irrespective of the fact that you don’t have an FIRC. But you must collate for the documents proving that you have received the amount in foreign currency, like certificate from bank stating that you have received the amount in foreign currency (not FIRC), any other document proving the same, etc.
So, don’t worry, just compile the documents.