How did you use four controllers?
To be honest, I never tried using the web version. However, when playing with PICO-8, I just have them connected to my computer and it worked fine. I didn't have to do anything special. In terms of code, when detecting button presses, you can use a second parameter (0 through 4) to ask for that button press for a specific controller. For example, btn(0, 2) gets the left button (0) from player 3's controller.