MEMS pressure sensors are widely used in several application fields, such as industrial, medical, automotive, etc, where they are required to be increasingly accurate and reliable. However, these sensors are very sensitive to mechanical and temperature variations. For example, the soldering process, which involves significant thermal stress, causes drift in the sensor accuracy. This article introduces a digital circuit implementing a very tiny neural network able to compensate for the drift measurement in real time. The circuit is capable of correcting for drift accuracy up to 1.6 hPa, restoring the accuracy to $\pm 0.5\ \text{hPa}$. Synthesis results on TSMC 130 nm CMOS technology show an area occupation of 0.0373 $\text{mm}^{2}$ and a dynamic power of 1.07 $\mu \mathrm{W}$, which enable its easy integration in the digital circuit which is available into MEMS sensor package for pressure measures conditioning.