I have a simple HTML page which has a Textbox and a Submit Button. I have a Azure Function which when hit takes in the content of the textbox, which we should send to the Az
This is definitely a CORS related issue. Luckily, it's easy to configure CORS for Function Apps in the portal. Just navigate to your Function App and then select Platform Features:
Select the CORS option under API which will take you to a screen where you can add the hostname of your clientside application: