No: going back to save them would have caused a paradox and ripped the world apart.
From the episode's transcript:
DOCTOR: Back where we started. You collapsed the timeline. The paradox worked. We all pinged back where we belong.
RORY: What, in a graveyard?
AMY: This happened the last time. Why always here?
DOCTOR: Does it matter? We got lucky. We could've blown New York off the planet. I can't ever take the Tardis back there. The timelines are too scrambled. I could have lost you both. Don't ever do that again.
RORY: There's a gravestone here for someone with the same name as me.
(Rory vanishes. There was an Angel behind him.)
DOCTOR: I'm sorry. Amelia, I'm so, so sorry.
AMY: No. No, we can just go and get him in the Tardis. One more paradox.
DOCTOR: Would rip New York apart.
DOCTOR: You are creating fixed time. I will never be able to see you again.
AMY: Raggedy man, goodbye!
(Amy turns her back on the Angel, and vanishes. Rory's gravestone gains more words - And His Loving Wife Amelia Williams aged 87.)
Out of universe, of course, it was time for Karen Gillan and Arthur Darvill to leave the show, and this was a fancy and poignant way of separating them from the Doctor forever.