If that directivity you wanted to achive is OK (this means the angle over which the power is radiated, mainly) then is only matter of efficiency.
You reached -2.056dB, that is 62%. Usually patch antennas have efficiency ranging rouglhly from 50 to 90% then you are inside it. This depends from factors like substrate losses, material conductivity, etc.
However if you could increase the efficiency up to the ideal 100 % the gain will increase 10*log10(100/62)=2 dB; not so much.