I would expect some kind of filter to exists on website or in console.
This isn't easy right now, unfortunately. There's an issue open on the NuGet Github about adding a filter to the website.
Right now, the best way to tell if a package will work with .NET Core is by examining the frameworks it supports in the Dependencies section.
If .NETStandard is listed, the package supports .NET Core via the .NET Platform Standard:
If a package's Dependencies section doesn't mention .NETStandard, or the Dependencies section is completely empty, it does not support .NET Core: