Toilets are designed to flush properly and completely when the reservoir/cistern/tank is filled to the design height/level/volume. When you leave the level lower than its design height you reduce the volume and water-column pressure of the flush water.
In the "old days" when toilet tanks had a lot of water (like up to 3-5 gals.) this wasn't usually a big deal. Currently most toilets are designed to "save water" by utilizing less flush water, leading (IMO) to some toilets that barely flush effectively. Any reduction of flush water in these can lead to partial or ineffective evacuation of bowl contents. You need to raise the water level to its design height.
If you have ineffective flush performance with the water at the design height, then the most likely problem would be a partially obstructed toilet bowl outlet path.
Experiment by filling a bucket with plenty of water and dumping it quickly into the bowl, to see if it flushes.