Engine knocks when acceleration padel is depressed

In my Vitz 2006 automatic transmission car, it works fine when cold that is the car accelerates normally feeling the power with respect to the depressed accelerator. After a journey of 10 to 15 Km's specially when car goes in the narow streets the car starts knocking when accelerator is depressed to increase the speed lets say from 15Km's/hrs upword.
The knocking sound comes from engine and to reduce the knock I have to stop pushing the accelerator pedal and slowly pressing it again until the car speeds up. I have learnt one thing with expeience that when the engine starts knocking I shift the automatic gear to "S" postion from normal drive "D" position. I can immediatly feel the power and there is no knocking sound but after gaining speed upto 50 to 60 Km's it gives you the sound that the engine is runnung in low gears so I have to change it back to "D" again and it works fine till I reduce the speed around 15 to 20 Km's and then the same knocking will appear again.
Please note their is no engine check light on the display.
I have done the following things to rectify the fault but no results.
I have changed engine oil, sparkplugs, airfilter, oil filter.
Throtal body was cleaned.
In idel condition when engine is running while pressing the acclerator I have checked the exhost and I have seen no smoke.
Please help me out regarding the problem.