Its difficult to say, if you made a mistake on the river, when you dont tell us either the action or the effective stack size. If stacks were reasonable short, then this is probably just a cooler, but if they were deep, then its certainly possible to not go broke with a T high flush on a paired board. So why not post the actual hand history next time, so you can get much better feedback.
The other thing I would suggest you is to play draws more aggressively in general. It was a limped pot, so leading the flop would certainly be a reasonable strategy, or you could go for a check-raise. Check-calling with a draw out of position is generally the worst of any possible line other than maybe folding. The point is, you have T high, and by just checking and calling you dont give your opponent a chance to fold.
And to be honest with you this passive style of play is probably a much bigger part of the reason, why you lose, than coolers like running a flush into a full house. Coolers happen to everyone, and just as often you will be the guy with a full house, when someone else has a flush.