These are the exact kind of players you should be patient against. If you realized that this opponent was ultra-aggressive, or played and was successful (or lucky) with mediocre hands, you should have used this information to crush him. Instead, you pushed with an average hand, had the fortune of being in better shape than you should have been (had his J 9 dominated), yet still got extremely unlucky.
I imagine the tournament this occurred in was a freeroll, but you still have to use your opponent's play against them. Pushing with J 10 wasn't the right hand to confront him with. Wait for A's, K's, Q's, or A K and put your money in the middle knowing you're more than likely the pre-flop favorite. If you still get outdrawn, take satisfaction in knowing you put yourself in the best situation possible to double up, yet was unlucky to lose.
The best players don't always win every tournament they play, but what they ALWAYS do is put themselves in the best situations possible to win even though they lost.