This paper presents a sensitivity analysis of filter bank multicarrier (FBMC) systems to carrier frequency offset (CFO) and timing offset. Although the emphasis of the paper is on the class of FBMC systems that are based on offset quadrature amplitude modulation (OQAM), the developed results are found applicable to cosine modulated-based FBMC systems as well. We assume that coarse CFO and timing offset estimations and compensations have already been performed so that the residual CFO and timing offset are small. A simple closed-form approximation to the signal-to-interference ratio (SIR) is derived. This approximation is compared numerically with the exact SIR and confirmed to be accurate for a variety of FBMC systems with different prototype filters. The derived SIR is characterized by a pair of coefficients that are only dependent on the underlying prototype filter, thus, allows the designer to pick from the choices of the prototype filter the one that has minimum sensitivity to CFO and/or timing offset.