It is not because of the manual mode unless you know what setting you really need. Most of the photographers rely on the light meter to determine the correct exposure. However, if the light meter give you a wrong reading (because it does not know what you really want to capture), auto or manual mode will yield the same result since it based on the same light meter readings.
However, based your experience (like from this photo), you know the camera light meter (in matrix mode) will give you a underexpose photo, so next time you may dial the exposure compensation to +1 or +2 (if your camera has this feature). And if your camera also has a "Spot Meter", the light meter readings maybe more accurate in this situation.