So the entire pool shell was left intact other than those three holes in the bottom? How large is the pool? The best solution would have been to break most of the bottom layer up, that way the water had multiple paths to leave.
Again, it depends on the size of the pool vs the area removed for the holes, but think of it as a sink with 3 drains that have been clogged up. The water is running out once it reaches those holes, but it has to get to those holes. The slope of the pool floor and the dirt composition surrounding it can limit it's path. And so, if those holes are backed up or have compacted, there is no where else for the water to go but up.
The easy (at least without digging it back up) answer would be to set up some sort of drainage system. Considering you had a pool and patio there though, I'd guess it's all relatively flat land though and so again there isn't many options for the water to run to nor easy way to do it.
I believe you're going to have to have it dug back out and finish off that pool floor with a jackhammer or such.