Yea you should have but that's a hard spot to be in. Another thing that you could of done is not bet on the turn and checked it. This makes it so that if he has a jack, he will define his hand by his action. Also, it could look like you had the jack if he thought you were bluffing with the bet on the turn. Which would explain why he min raised you on the turn if he was bluffing.

I can't say whether he had the jack or not because you don't really know but, you always want the other person to define their hand so that you can get some information and make an appropriate read on your opponent. At least this is what I've been told..