The detection of gravitational waves by the first generation of ground-based interferometric detectors, like LIGO, relies on sophisticated data analysis techniques. For the inspiral phase of binary compact objects, the optimal one is the so-called matched-filtering technique. The output of the detector is cross-correlated with a bank of templates. The closer the templates are to the real signal, the higher the S/N of the detection is. In this paper we quantify the loss of S/N that occurs when one tries to detect a precessing binary using non-precessing templates. To do so, we compute the fitting factor which is a measure of the mismatch between the signal and the templates. The precessing signal is obtained using a 1.5 PN analytical approximation of the real solution called simple precession. We found regions of the parameter space for which the detection could be jeopardized if precession is not accounted in the templates. The solution of this problem could be to use more complete templates, that could capture the main features of the precession. Specifically we examine such a family of 'mimic' templates, that requires only three additional parameters, first proposed by Apostolatos. However we find that this family does not recover the main part of the signal. We conclude that a more efficient template family will be needed in the near future.