The rating for your website on services like Google PageSpeed might indirectly affect how your website rank in the serp. One area that Google PageSpeed measures is how well you have optimized your images. You should therefore optimize your images to keep up your rank in the serp.
Myself I use several techniques for that.
One is the PHP-script
image.php which helps me scale and process the images serverside, including running extra tools for image optimization during the process.
Another useful tool is to check the
/img directory and run a bash-script that optimizes the images of my selection.