Tony wasn’t sure if he should grieve or whether Terry was alive somewhere and he, Tony, should be putting all his resources into finding him. He’d already been responsible for executing two men, wrongly if his current instinct about Terry was correct. But then those two men were killed on Tony’s instincts... so maybe his instincts weren’t so good.
His current instinct could easily have been checked had he been prepared to go and identify Terry’s body. He didn’t trust Livia to tell him the truth... and somehow, if he didn’t see Terry’s body, he still had hope.