I am very confused.
I have created a Class Library using .Net Standard Library 1.6.1
There's no such thing as ".Net Standard Library 1.6.1". There is .Net Standard 1.1 through .Net Standard 1.6. And there's also the
NETStandard.Library 1.6.1 package. But the version of that package does not dictate which version of .Net Standard are you using.
using an assembly from .NET 4.1
There's no such thing as .Net 4.1. Did you mean .Net Framework 4.5.1 or 4.6.1?
I have created a Class Library using .Net Standard Library […] my application using an assembly from .NET 4.1 […]
How is the library related to the application? How does what the application does affect what the library can do? Can't you upgrade the application to a newer version of .Net Framework?
having the same result
What actually is the result? Could you explain what exactly did you do and what did it do?
Looking at the table I've suggested that .NET Standard 1.6.1 uses .net 4.6 libraries
.Net Standard does not use .Net Framework libraries at all. And what the table says is that for example a .Net Standard 1.5 library can only be referenced from a .Net Framework 4.6.2+ project (only look at the "with tooling 1.0" row). But since it's not clear to me what version of .Net Standard or .Net Framework are you using, I can't tell you the specifics.