Brake pressure is there when the engine isn't running, but as soon as you've got servo assistance ... . You might have got one of your pistons stuck in the caliper as you pressed it back in. Brake Cleaner spray ... invaluable.
Surely if the piston get's stuck then the new pads would not fit, unless the piston was all the way in before becoming stuck. You should have some brake even so as the other brakes would still be activated.
You may need to bleed the brakes several times and ensure that your master cylinder is topped up to max before and after bleeding. You may have bled the brakes to the point where the fluid level in the master cylinder became so low that you sucked air into the system.
Truthfully, if you don't open the system, there should be no need to bleed the brakes as I'm assuming the master cylinder had fluid in it before you started the job so as you pushed the pistons back in, the fluid in the lines would have been forced back into your master cylinder. In fact I have seen it where the master cylinder has overflowed once the pistons have been pushed back in due to the addition of fluid before you got to the point where you decided to change the brake pads.
If all the pads are in their proper place both inside and outside pads on all four wheels, remove the wheels while supporting the car on jacks or axle stands and have someone start the engine and slowly operate the brakes so that you can see if there is any movement of the pads. If not, and there are no leaks and no air in the system then it could be an internal leak in your master cylinder that may have prompted you into changing your pads in the first place thinking they were worn down to the point of needing to be replaced..
A bit of a pain to remove and replace but not really all that difficult to do with the right tools. If that is the problem I would suggest going for a rebuilt master cylinder rather than buying the kit to rebuild it yourself as the bore may need to be honed and that can be a pain in the arse, including that you have to ensure that you don't leave any sh!te inside the cylinder bore which will cause it to leak again as it damages the seal.
It's really hard to say what could be wrong other than what's already been suggested without actually being there and seeing things in action.