Between 2004 and 2009, a sample of 28 X-ray selected high- and intermediate-frequency peaked blazars with an X-ray flux larger than 2 μJy at 1 keV in the redshift range from 0.018 to 0.361 was observed with the MAGIC telescope at energies above 100 GeV. Seven among them were detected and the results of these observations are discussed elsewhere. Here we concentrate on the remaining 21 blazars which were not detected during this observation campaign and present the 3σ (99.7%) confidence upper limits on their flux. The individual flux upper limits lie between 1.6% and 13.6% of the integral flux from the Crab Nebula. Applying a stacking method to the sample of non-detections with a total of 394.1 hr exposure time, we find evidence for an excess with a cumulative significance of 4.9 standard deviations. It is not dominated by individual objects or flares, but increases linearly with the observation time as for a constant source with an integral flux level of ~1.5% of that observed from the Crab Nebula above 150 GeV.