Heat a grill to medium-high heat. Place the portobello mushrooms in a dish or pan and rub the balsamic vinegar and olive oil onto both sides of each with your fingers; use just enough of each to coat evenly. Let sit to marinate until the grill is ready.
To serve, place a mushroom on one half of the focaccia bread; top with tzatziki sauce, red onion slices, feta crumbles, and the other half of of the bread.