I have a one story house on a flat lot with no basement. A few years ago I had a patio put in the back. Ever since then, I have had problems with water seeping into the house under the foundation slab during heavy rains. The result is wet spots on the carpet. Before the patio, everything was fine. I have tried caulking and even had part of the concrete replaced with no results. I have no drainage system or gutters in the back. Maybe that is what I need. Please advise. Thank you.

The patio must slope away from the house, hopefully you have that? You also need to have a step up from the patio to the slab of at the very min. a couple of inches especially at the doors if this is low you can try sealing between the bottom plate & the slab at the exterior and across the thresholds.

First try a simple solution (below), then if this doesn't work you'll need to go to a more drastic measure of removing a section of the patio & placing proper flashing & or seal at the main house, drain rock to below frost & drainage.

The joint between the patio & slab should be cleaned of all previous sealants. To do this well you may need to use a masonry grinding wheel. The crack should be cleaned to a depth at least equal to the width of the joint. If it is deeper,insert polyethylene backer rod in the joint to make it the same depth as it is wide. Then fill the joint with an elastomeric caulk. Polyurethane is a good choice. With some types of caulk, it is necessary to coat the edges of the joint with a primer for good adhesion. Follow the directions of the caulk manufacturer.