I encountered the same problem, and tried the 777 work-around mentioned by Brian07002 as a temporary fix, to troubleshoot. (777 means that anyone and everyone can install and execute programs there!) Once I’d installed simple:press, I checked to see who owned the newly installed items. The listed owner was the group, “www-data.”
In summary: at least on my machine, simple:press expects /wp-content to belong to www-data, but it actually belong to root.
Workaround: in a terminal in your WordPress directory, change the group for wp-content and its contents to www-data (sudo chgrp -R www-data wp-content/) and change permissions to 775 (chmod -R 775 wp-content/). That allows both root and members of www-data to read, write, and execute files, but does not allow strangers or intruders to do so.
I have not figured out why the owner of the WordPress folders is root while the owner of the simple:press folders is www-data. I suspect that there is a better work-around that mine, but 775 is safer than 777, so I thought I’d post.