The problem with tea is that it has tannin and tannin likes to soak into cotton and other things. We can deliberately dye cotton with tea and coffee, and we use heat among other things to set that. It's like toast, you are using heat to carbonize the bread and once it is toasted you can't untoast it.
But -- especially if you normally use things like dryer sheets or fabric softener, or there is a blend in the fibers (even a small amount of poly can keep dyes out) it is possible that the stain is still around and not in the fibers. So try a warm/cool soak in Oxyclean. If you have any basic Dawn dish soap, rub some in and soak with that for awhile and then rinse until clear. Do not put dish soap in your washing machine. Just don't do it -- it is much funnier on I Love Lucy than in real life.
If you've already tried once, I'd try one of these other things and then move on. Or use that shirt to paint in. Or maybe do some tie-dye with it.