I have added a feedback module and setup the Feedback recipient as follows:

1. Add a Feedback module, or go to an existing Feedback module.2. Select Settings from the module menu.3. At Feedback Settings click the Maximize button.4. In the Send To field, enter the email address of the recipient of feedback sent from this module.5. Click Update.

When the user fills in the details and presses the send button the following message is displayed

Your Message Has Been Sent 

But the recipient does not get the Message

When the Admin goes into “Feedback Moderation” it shows all the messages that were sent  (but the recipient has received any of them)

Is there some setting on the Host Server that I must set?

you should also try to send an email using same user and manually entering admin email as recipient in Admin :: Newsletter module.

If you log in as Host on your DNN site, you can navigate to Host Settings which has an option to check the SMTP settings. If you don't have the Host username/password, I'd ask your administrator to confirm this works for you.
Sanjay