Nerves will do that!
So many people leave interviews realizing what they "should have" said. Live and learn. You can still try to negotiate, though--no harm in trying. Yes, he could remind you that he is offering more than your stated minimum. You could, however, say that after thinking through the position (and perhaps other offers, if applicable), you believe a fair salary would be X. If the 38k is reasonable to you, though, I wouldn't push it too far (after all, it is still more than you originally wanted). After you have proved yourself to the company, you should have room to further negotiate. In fact, you could ask for a six-month salary review if he doesn't budge on the initial offer.