How to click faster in puzzle rush / puzzle battle?

I watched titled players doing puzzle battle match and I was amazed at the speed. 

One thing was of course that the speed of recognizing the solution was much higher than mine.

But I also the speed of moving pieces also seemed unreal. 

So the question is, how to increase speed of clicking?

I tried with a mouse on computer screen but the moves with a mouse are quite substantial and seem to require training to be accurate. 

Then I tried doing puzzle on the phone and I felt that I can move pieces faster, but still nowhere close to the speed of title players.

So what's the best way to click faster? What hardware is the best? 

theres no shortcut, train your pattern recognition, train your mouse speed.