Yes, the pictures need to be compressed and optimized for a website. That's why I have to make due with the "Save for web & devices" function until I can get a hold of a newer version of Photoshop.
I'll use the option to reduce img size to get it to a decent size for web.
As an addition I asked the folks from the Shortpixel plugin for Wordpress if they suggest to send already via PS optimized pictures through their plugin to upload or just upload the unedited file.
They even said to use the original unedited picture because it has better quality, as long as the file size is under 50MB. I saw instances where they actually reduce file size for web by 95% or more (choosing lossy compression). I think this is quite decent.
Cheers,
Stan