Why was The LEGO Movie not nominated at the Oscars?

Here's a Variety article on this very thing with 5 reasons:

“Lego” landed just one mention — in the song category for its infectious “Everything Is Awesome” anthem — but not in the animated feature category, where many were predicting that the toon blockbuster might win.

That oversight comes as a total shock to Oscar pundits — arguably the year’s biggest snub, alongside the fact that “Selma” placed in only two categories (for which theories abound). From the point of view of the animation community, however, there was always a risk.

The reasons reported are as follows:

1. Animation professionals pick the nominations
2. A record number of eligible toons means tougher competition
3. Voters watch all 20 contenders, so the best rises
4. The animation branch loves handmade movies
5. Traditional forms and classical storytelling win out

The original report is here:

5 Reasons the Academy Overlooked ‘The LEGO Movie’

Looks like there is no one overriding answer, it was a combination of things. Given Variety's place in Hollywood I would imagine it's pretty accurate.

I don't have the minute count for the film but the rules require:

An animated feature is defined by the academy as a film with a running time of more than 40 minutes in which characters' performances are created using a frame-by-frame technique, a significant number of the major characters are animated, and animation figures in no less than 75 percent of the running time.

It's possible that the live-action sections added up up to over 25% of the film's content, and caused it to be out of the running.

That being said, I have a difficult time believing, from my memory, that the live-action portion was 25% of the film.

Edit:

As noted by Ankit Sharma in the comments, my memory is correct. The film was 100 minutes and the live action section was only 10 minutes long, making it only 10% of the running time.

This means that this technical reason is not a possible explanation for why the film wasn't nominated.