If your only option is to change background-image like mine, this is what worked for me:

1. From fontawesome's webpage, click the icon, select svg and copy.
2. Fontawesome icons don't have color, you need to change the color as explained here: How can I change the color of an 'svg' element?
3. Now your problem is "how to use an svg as a background-image, which is neatly explained here: Using SVG as background image

then you can just use something like below:

.my-class {
   background-image: url("data:image/svg+xml,%3Csvg%20xmlns%3....");
}

This worked like a charm!