If you're not shooting for a living, then low light photography is fun in itself because of the challenges it poses.

I agree with Sabyasachi's suggestions. The Tamron 150-600 has a very good VR system, so you could easily have tried a lower shutter speed. With the right handholding technique, you should be able to handhold at 1/double-digit shutter speeds at 600mm with that lens. Secondly, a wider aperture means everything in low light, so go for the best focal length at the widest available aperture. You can even use low light to make some creatively blurred images.

Of course, if very sharp shots matter a whole lot to you, then more capable cameras and faster lenses are the answer.