Hi Thomas,
>> Unfortunately, I get the message that I don't have sufficient permissions.
Based on this error message, I assume you do not have the permission to create an Access web app in your SharePoint. Access web app inherits the user permission from SharePoint site. I suggest you contact the administrator of SharePoint site, and assign
the correspond permission like Edit or full control. You could refer the link below for user permissions.
# User permissions and permission levels in SharePoint 2013
https://technet.microsoft.com/en-us/library/cc721640.aspx
Best Regards,
Edward
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