They can, but at any given
sample size, there is a minimum effect size to achieve statistical significance. Larger effect sizes are always more significant, and smaller effect sizes are always less significant.
So if you assume they wrote the paper after doing their work, and not before, the sentence makes perfect sense: the work is already done, there is an effect size cutoff for statistical significance, and they didn't reach it.
One of Andrew Gelman's frequently-mentioned points is that a statistical significance filter in publishing means that published effect sizes are almost always wildly overestimated, precisely due to this effect.