Using singleton for caching

I recently read that singleton is an anti-pattern and should not be used unless it is really needed.

In all our projects, we use the singleton pattern to hold some cache data. For example:

class SomeClass
{
   public SomeClass()
   {
       var somedata = Singleton.Instance.GetSomeData(stringRepresintation); // or like that
       var someData = Singleton.Instance.SomeData;
   }      
}

What is the recommended design to hold that data (static class, or something else)?