Uncomfortable saddle position on road bike. I ride a road bike three times a week (Bitten by strava bug)( I am 5'9" and use a 54 cm frame)

I installed my new pedals and am wearing my new cycling shoes for first time. I raised the saddle height few centimeters hoping to match the rise in height due to cleats.

Also, i moved my saddle towards the stem to accommodate the height change, for some reason my saddle is a real pain. I feel uncomfortable and have to focus constantly on setting myself on saddle rather than focusing on the road ahead. 

I think this also is pushing me back in terms of giving my best on the road. I have tried using methods like leg seam length, knee slightly bend method to try adjust the saddle and it doesn't seem to work. 

Has anyone of you also faced this problem and what did you do to fix it ?
Are your cleats "a few centimetres" thick? It seems unlikely! It's hard to imagine that your cleats put your foot more than a centimetre farther from the axis of the pedal than was the case with your old pedals, so the simple conclusion is that you moved your saddle way too far.