Do you mean to say Inter Milan aim was not to win the trophy? I don't know why people think it would have been different with Barcelona in the Final, if they were so good why couldn't they win Inter Milan and progress to the Final.
I think they are still inexperienced and nothing would have changed if they had been in the Final, PSG would have equally won them the only difference would be the goal margin and probably they'd be able to score a goal or two as well. In my opinion the best team won and nothing would have changed no matter who they faced because they played against top teams along the way and still came out victorious.
I am really impressed with how Luis Enrique transformed the team, I hope to see them with the same top performance next season.
All clubs want to win trophies but with different financial resources as well as their temporary financial statuses, they must have different strategies for their club development and operation from competitions to financial management. It's easy to spend money you have and even borrow money to do something but history has enough painful lessons from clubs that did overspent then got massive financial crisis later, including bankruptcies like Leeds United, Deportivo La Coruna, Fiorentina, Lazio, Napoli and more.
Inter Milan truly wanted trophies and will continue to aim at winning titles but they have to take their finance into consideration for any actions on transfer market for players in and out as well as salary ceiling in their club. They have been succeding in building up a competitive squad but it seems not enough for winning UEFA Champions League. A next season will be very challenging for Inter Milan as they no longer have Inzaghi as a head coach while a replacement is Chivu who is very young and lack of experience in this important position.