The director talks about the inclusion of I'm Not Crying in the film:
One of my favorite parts of the movie is a song from this band called Flight of the Conchords. I’m just curious how you went about getting that and what their reaction to being approached for this.Source
The interesting thing is that this book, and this screenplay’s written by a guy named Gideon Defoe. He’s a young Englishman… I bet he’s about the same age as the Flight of the Conchords. They just share a sense of comedy. Just coincidentally. They didn’t know each other at all. They have a very similar sense of comedy. I was a big fan. I loved their show. Such a funny act they had. So, two things. One is that we approached them to write the title song. Never actually happened, unfortunately. We couldn’t get it right. We tried. We tried many times; couldn’t get it right. But we love their music. It’s hard to remember, but somebody went through their back catalog of music and found this song and put it in there, just in the early days.
Yeah, temp music. When it was all in drawings. Temp music, that’s right. Everyone just loved it. ‘That’s so charming. Well, we’ll stick with that.’ And we did, through thick and thin. Often in animated movies, you’ve got so long to make the movie that there’s a great danger that you undo good stuff. You have a great idea and everyone goes ‘Hahaha. That is a brilliant idea.’ Then you live with it for two years and at the end of two years you think, ‘That’s a crappy idea.’ [All laughs] So you have to say, ‘No, no, wait, we all loved that one. Have faith.’ So we stuck with it.
It’s funny, actually, because then we ended up with a music supervisor, who’s a guy basically who’s job is to offer up potential tunes and he offered up some straight sad songs, and they worked… of course they worked, but it was wrong for the film. So I’m so happy to have this witty sad song. There’s some great stuff in there. There’s The Clash in there and there’s also a song that I chose, in particular, that nobody notices. But it’s some crazy old coot, sitting on his front porch somewhere in the mountains in American in the 1920s playing a guitar and singing ‘I’m sailing on the ocean.’ It sounds like a million years old. Makes me laugh. So we had fun with the music.
It's a shame the title song didn't work out but it sounds like I'm Not Crying was a perfect fit.