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[Abridged] Context. The CoRoT space mission has been searching for transitingplanets since the end of December 2006. Aims. We aim to investigate thecapability of CoRoT to detect small-size transiting planets in short-periodorbits, and to compare the number of CoRoT planets with 2 \leq R_p \leq 4Rearth with the occurrence rate of small-size planets provided by thedistribution of Kepler planetary candidates (Howard et al. 2012). Methods. Weperformed a test that simulates transits of super-Earths and Neptunes in realCoRoT light curves and searches for them blindly by using the LAM transitdetection pipeline. Results. The CoRoT detection rate of planets with radiusbetween 2 and 4 Rearth and orbital period P \leq 20 days is 59% (31%) aroundstars brighter than r'=14.0 (15.5). By properly taking the CoRoT detection ratefor Neptune-size planets and the transit probability into account, we foundthat according to the Kepler planet occurrence rate, CoRoT should havediscovered 12 \pm 2 Neptunes orbiting G and K dwarfs with P \leq 17 days in sixobservational runs. This estimate must be compared with the validated NeptuneCoRoT-24b and five CoRoT planetary candidates in the considered range ofplanetary radii. We thus found a disagreement with expectations from Kepler at3 \sigma or 5 \sigma, assuming a blend fraction of 0% (six Neptunes) and 100%(one Neptune) for these candidates. Conclusions. This underabundance of CoRoTNeptunes with respect to Kepler may be due to several reasons. Regardless ofthe origin of the disagreement, which needs to be investigated in more detail,the noticeable deficiency of CoRoT Neptunes at short orbital periods seems toindirectly support the general trend found in Kepler data, i.e. that thefrequency of small-size planets increases with increasing orbital periods anddecreasing planet radii.

Detection of Neptune-size planetary candidates with CoRoT data. Comparison with the planet occurrence rate derived from Kepler