Search API requirements
You can't use facets on MySQL (for the moment), from the project page:

Search facets
This module provides the ability to create facets on any search executed anywhere in Drupal, be it a search page, a view or any other source. The feature isn't available for all servers, though, since it would be too complex to implement for some service classes. Right now only the Solr servers support this, facet support for the database-based searches might be done in the future.

This means that you can't use facets, but you can still use Search API to search your content.