What do you mean by "the whole thing fell apart"? Do you mean strips that had previously been sewn together became unsewn and therefore you think you should have used a smaller stitch?
I'm not getting something.
I've done more than a few Bargello, most with at least a few 1/4" strips.
One recommendaation ... are you sewing each successive strip in the opposite direction? What I do is leave the thread tail on my start end so I know which end I started, then the next strip I sew in the opposite direction. All the ends are going to be cut off anyway so leaving the start tail on is not a big deal (as long as you keep it out of the way while your sewing).
Also, are you using starch? helps a lot.