Some additional configuration may be required if you use private dependencies not hosted on the default registries, depending on package manager.
For maven your .m2/settings.xml needs to be configured for the specific registry you wish to use, see the settings documentation for more details.
Using Azure Pipelines this can be done by commenting out the authentication step in the template.
More information about this can be found here.
Just like with maven you need to configure access to private registries or sources, see NuGet's documentation on source mapping for more information (and the authenticated feeds documentation for details). When using Azure pipelines your authenticated feeds can be accessed by commenting out the NuGet parts in the default template (see nuget authenticate documentation for more information).