Of course normally Inter would target multiple trophies. Even the Champions League too considering they qualified for the finale there 2 times in the last 3 years. But here is the thing...
We don't know what Chivu can do in his first season. He isn't as experienced as Inzaghi. At first their main target would be to bring the Serie A trophy home in my opinion. If he competes well for it then the expectations would surely get bigger than that.
Chivu is young and may lack experience especially in the Champions League, but apart from that even winning Serie A would be a great achievement and I think it would be the right goal to focus on one competition and try to win it because the problem for Inzaghi was that he tried to win everything at once but he couldn't win anything. In the end he started to prioritize the Champions League and Napoli were able to take advantage of that. And now they are losing points already at the very beginning against Udinese and if they can't win against Juventus it will be an indication that Serie A will be more difficult for them than it was with Inzaghi.