[Abridged] Context. Spectral differential imaging (SDI) is part of the observing strategy of current and future high-contrast imaging instruments. It aims to reduce the stellar speckles that prevent the detection of cool planets by using in/out methane-band images. It attenuates the signature of off-axis companions to the star, such as angular differential imaging (ADI). However, this attenuation depends on the spectral properties of the low-mass companions we are searching for. The implications of this particularity on estimating the detection limits have been poorly explored so far. Aims. We perform an imaging survey to search for cool (Teff<1000-1300 K) giant planets at separations as close as 5-10 AU. We also aim to assess the sensitivity limits in SDI data taking the photometric bias into account. This will lead to a better view of the SDI performance. Methods. We observed a selected sample of 16 stars (age < 200 Myr, d < 25 pc) with the phase-mask coronagraph, SDI, and ADI modes of VLT/NaCo. Results. We do not detect any companions. As for the sensitivity limits, we argue that the SDI residual noise cannot be converted into mass limits because it represents a differential flux, unlike the case of single-band images. This results in degeneracies for the mass limits, which may be removed with the use of single-band constraints. We instead employ a method of directly determining the mass limits. The survey is sensitive to cool giant planets beyond 10 AU for 65% and 30 AU for 100% of the sample. Conclusions. For close-in separations, the optimal regime for SDI corresponds to SDI flux ratios >2. According to the BT-Settl model, this translates into Teff<800 K. The methods described here can be applied to the data interpretation of SPHERE. We expect better performance with the dual-band imager IRDIS, thanks to more suitable filter characteristics and better image quality.
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