R3 and C1 form a high pass filter that has a 3dB point at 22 Hz so this isn't causing your low frequency problem. Maybe you need to explain what you used to stimulate the microphone?
At the high end of the spectrum C3 and R4 (if the components used are shown correctly) produce a high frequency low-pass 3dB point at about 16 kHz so there's no real problem here. Again, I ask what you used as your audio source.
I've just seen your comment that you are using your phone to produce sound stimuli and I hang my head in despair that you believe that your phone can adequately produce accurate sound pressure levels to calibrate a microphone with. Go do some research on what your speaker can output.
Here's the frequency response of a speaker that is suitably sized to fit in a cellphone: -
Between 200 Hz and 1.2 kHz the SPL output changes about 50 dB. Taken from this report by Murata. Now clearly a speaker like this is going to sound tinny and there will be some attempt to offset this by electronic circuits that can emphasize the deficiencies but you are still not going to get anything like a flat response that is at all usable to calibrate your microphone.
Your microphones specification is 60 Hz to 15kHz +/-3dB is far better than what your cellphone speaker will be.