In this paper, we devote ourselves to interpreting the short-lived absorptive type III-like microwave bursts in the 2006 December 13 flare event observed with high temporal and spectral resolutions (8 ms and 10 MHz) by the Chinese Solar Broadband Radio Spectrometer (SBRS/Huairou) at 2.6-3.8 GHz. In the decimeter-centimeter wavelength range, we first present the observations of short-lived bursts represented as a number of absorptive ``spikes'' superposed on the type IV continuum that can be connected by fast-drifting lines. The mean drift rate, the instantaneous bandwidth, and the absorption depth of these absorptive spikes are about -12 GHz s$^-1$, 70 MHz, and 40%, respectively. The duration at a single frequency band can be less than the instrument resolution of 8 ms. On the basis of numerical investigations of the loss-cone instability, we suggest that fragmented electron injections with durations of as short as several milliseconds into the loss cone could be the most appropriate mechanism with which to explain the bursts. The length of an electron beam is estimated to be about 400 km, on the basis of the observational results. These injections may be related to the fragmented energy release processes during the flare. We also observe some absorptive type III-like bursts accompanying ordinary type III bursts with reverse drifts. They start at the same frequency, and the starting frequency slowly drifts to the low-frequency region. This could be a signature of propagating bidirectional electron beams originating near the reconnection region.