As far as the on-screen reaction to its destruction went, I don't think anyone on that crew, even Riker, felt for the ship what the TOS crew felt for their Enterprise. Considering the Stargazer was the ship Picard served on for over two decades (and he expressed great affection for it), and the E-D wasn't his first command, I could see why he may not have been that emotionally attached to E-D after only seven years on it.
Yeah, I can totally buy that.
But you would've thought there might've been some repercussions to Picard. This is the second ship under his command that he's lost. Wouldn't he have faced a court martial or something? Would they have kept the crew together? I dunno. Those are some of the questions I had.
His starship insurance premium would certainly go up.

In FC Picard faced repercussions from his contact with the Borg. But I see your point about losing two starships and going on with an "oh, well" attitude. That does take some explaining, and at least a hearing to investigate any faults in command would be in order. Then again, Riker was technically in command of E-D (in the chair at least) when it was lost. And for all we know, a hearing was held, and Picard (and Riker) were exonerated for what happened.