SHINJI:“(---pause---)Don’t…don’t say you don’t have anything else……don’t ever say...”
Kendrix: He couldn't quite think of what to say, and so, he talks of the words that have shocked him so much before the battle began.
Leighton: I find what Shinji says here is a contrast to what Gendo says. Gendo just says "Good"; I get the implication that he's just worried if Rei is still alive or not.
For Shinji's case, it provokes a more emotional response. I think for the first time Rei is personally valued to another, particularly in contrast to Gendo's value of her as an ingredient for his version of instrumentality. You could say, Shinji feels Rei's pain and wants to show it. I think its also the first time he's crying as a result of care rather than anger.