Release management does not have a container for build artifacts, that's why you see this error message.
You can try with following task:
Write-host "##vso[task.uploadfile]<filename>"
View and download attachments associated with releases
Would you like to upload additional logs or diagnostics or images when running tasks in a release? This feature enables users to upload additional files during deployments. To upload a new file, use the following agent command in your script:
Write-host "##vso[task.uploadfile]"
The file is then available as part of the release logs. When you download all the logs associated with the release, you will be able to retrieve this file as well.
You can also add a powershell script task in your release definition to read the log files and output it to the console. Then you will be see the content of the log files from "Logs" tab powershell script step. And you can also click "Download all logs as zip" to download the logs.
I'm not sure this should be marked the answer. Sure you can upload the logs like this, but you can't download them. "Download all logs as zip" only gives the use the VSTS logs from each step. How can we get the logs which were uploaded?
Scratch that, you need to refresh the page before the zip contains the uploaded files.
Do you know if there's a maximum file size that can be uploaded this way? I'm having problems getting this to work. It seems to work fine for a small zip file but a larger one (approx 40MB) doesn't.