While I agree that the Lego Movie deserved a nomination, it was definitely a tough year to squeeze it in, though if you were to ask me, I'd put it in over Big Hero 6. It was definitely a memorable movie, with all the puns, pop references, inside jokes, and muhh batman that I can see why it appealed to so many people. I for one can't stand super-hero characters at all, and I still found myself enjoying the Lego Movies take on the character. On the other hand, Big Hero 6 was a movie that probably deserved a nomination for the first half, but the second half was just so forgettable, and it was a shame to see a movie that could have been great just fall on its head like that.
On another note, the Lego Movie probably wouldn't have deserved the Oscar over Song of the Sea or Princess Kaguya, which are just better movies overall and both of which should have been in the running for Best Film if they didn't segregate animated and live action. If those two weren't nominated already, I could see it having a case, right up there with HTTYD2 and The Boxtrolls, but that isn't the case.