In Coleman's Aspects of symmetry he writes about significance of euclidean field configurations of finite action:

The naive anser, sometimes given in the literature, is that configurations of infinite euclidean action are unimportant in the functional integral, since, for such configurations, $e^{-\frac{S}{\hbar}}$ is zero. This is wrong. In fact, it is configurations of finite action are unimportant; to be precise, they form a set of measure zero in function space. This has nothing to do with divergences in quantum field theory; it is true even for the ordinary harmonic oscillator. The only reason we are interested in doing semiclassical approximations, and a configuration of infinite action does indeed give zero if it is used as the center point of a Gaussian integral.

I don't understand this. Precisely, I don't understand when semiclassical approximation enters the game. We use it when impose the Wick rotation, so I don't understand why the semiclassical approximation of the amplitude is different from evaluation of the euclidean path integral by using saddle point approximation.