Camera matching. Your 3D camera has to match your physical camera's angle of rotation and focal length. That clip you provided consist mainly of digital pans and tilts which makes camera matching a lot easier.
My suggestion is that you build a digital version of your physical set or at least build a reference set with key pieces that you can use to line up you 3D camera with. Use a pic of your stop-motion shot as the background in your 3D animation program and adjust your camera's position, rotation and focal length until it matches. The hardest part for me is the focal length. I used a Logitech 9000 for these shots, zoomed out so I assumed it was at 35mm. But it's not necessarily the case in the 3D program.
Best thing to do is practice. Take a pic of a LEGO piece on your table, set or counter (maybe a 2x2 brick). Do camera matching with a 3D 2x2 brick and add more 3D LEGO pieces around it, and see if it they look like like they belong in the shot (nevermind materials and shading).