Plants, like humans, can be very robust as adults, but as babies they need a bit of TLC. Most cuttings (of any plant) will droop and look very sad and forlorn for a while at first - in particular the tender baby parts at the tip of stems - until they form roots.

Don't give up yet. Just keep the soil barely moist, don't let it dry out at all, but make sure it isn't soggy. And cross your fingers.

Best and easiest solution is to forget taking cuttings altogether, and use pieces of the plant from under the soil. just hack off a bit of the original clump, complete with either roots or runners or both (don't worry if there are no above-ground bits), bury it, and sit back and watch it take off.