When replacing brake pads, brake loses its grip I wanted to replace my front wheel disc brake pads (Shimano BR-M785).

For the purpose, I removed the front wheel and removed the existing pads. Then I tried to place the new pads and found out the would not fit properly. 

After asking, I was advised to "push the pistons back to the callipers", This is, to use a non-metal device to push back to their place the two circular pressers (pistons?) that where outstanding preventing me from inserting the new pads.

Sure enough, after doing this I could install the new pads. Placed back the wheel and now when I brake there isn't enough pressure to cause any effect. The brake pedal is totally loose, as if there was nothing to brake with. Looking carefully, it seems that the pads are moving slightly and touch the brake disc, but nothing enough to make it brake.

Any advice? No liquid has leaked, nothing seems broken.

I'm sorry I don't know much about any of this, I though I could save some money doing it myself... seemed easy enough.

Thanks,
This may not be an answer but it was too long to comment.

When you compressed the pads did you open the system? Meaning uncapping the reservoir, or did you simply push them back without doing anything else? Sounds like air has gotten in the system and it will need to be bled. 

One of the steps of bleeding is creating a vacuum to pull air out of the fluid that isn't normally visible in bubble form. If the caliper pistons are pushed back without opening the system you may have done the opposite in a way and pressurized the system, then upon pulling the brake level you may have recreated a vacuum that pulled air from the fluid and caused an air bubble internally. That's the best way i can think to explain it anyway.

'Tis but a guess on my part but it sounds like a bleed is needed either way.

Pulling the brake while there is no pad or bleed block in there is also a no no and will lead to having to bleed the system.

Bottom line, bleed it or pay to have it properly done and i bet you're back in action. Also don't get fluid on the rotors or your new pads. and follow a proper bed in/burn in process.