Picasa app on Android is directly connected to the Picasa albums in the cloud storage, which means that if you use the browser to delete them, then they will be removed from the application as well.
You can login using the following link:
https://picasaweb.google.com/home
Note: Picasa depends on the Google Account, since it's a Google product, which means the account attached to your phone is the one to be used on the website.