You don't need to use the container in the unit test, the point of the unit test is isolated testing of the "system under test (SUT)" which in this case is your CustomerController
class.
What you should be doing is creating a mock implementation of your ICustomerRepository
which you supply to the constructor of the CustomerController
something like this:
[Test]
public void Customer_Index_Returns_ViewResult()
{
var customers = new [] { new Customer(), new Customer() };
var mockRepository = new Mock<ICustomerRepository>();
mockRepository.Setup(r => r.GetLatestCustomers()).Returns(customers);
//Arrange
CustomerController controller = new CustomerController(mockRepository.Object);
//ACT
var actual = controller.Index();
//Assert
Assert.IsInstanceOf<ViewResult>(actual);
mockRepository.Verify(r => r.GetLatestCustomers(), Times.Once());
}
This is based upon the Moq framework and a fictional use case based upon your example but should give you an idea to get you going.