You would think he'd be more torn up, but I think the movie establishes enough that Bruce is hellbent on a higher purpose, plus most of his emotions end up internalized, which is how his parents death created Batman.
One scene that I think establishes his "get the Joker" mindset is with Fox regarding the sonar gear. "I have to stop this man." "At what cost?" Lucius gives him a smack like hey, there has to be a line you don't cross to get the bad guys, but Bruce was hellbent on stopping him.
The fact to is, in a movie like this, you have to tone down the emotional impact of certain events simply to keep things moving. In reality, Bruce would have likely taken weeks to recover from that, but the movie circumstances didn't allow that.
I always felt Rachel's death was meant to have greater meaning anyway. Yes his best friend is dead, but it's the loss of Dent and Rachel and it's affect that matters, which is Bruce's chances for a normal life are slipping further away on him, can't have the woman he loves, the man who could take over for him is fading, and that's why the end is powerful for me, because he ends up saying ^^^^ it, I have nothing for myself, but I'm going to devote my life to a greater good, even if I'm hated, even if I have nothing for me, I'll do this because it's the right thing to do.