You have said it all. Inter underestimated PSG due to a lot of reasons. Firstly, they haven't win the trophy before and don't have the finals experience. Secondly, they struggled till they got to the finals and lastly, Inter defeated Barcelona who everyone sees as the best last season. I believe that Inter didn't even prepared properly for that finals. Assuming, they prepared for the finals the way they prepared when they played Barcelona, PSG wouldn't have humiliated them that way.
I don't think Inter Milan underrated PSG. The Italian side was already experiencing a drop in form before the Champions League finals. This was evident in their loss of points in the Italian Serie A, allowing Napoli to top the League. PSG was the clear favourite because they had a solid squad and had also defeated some of the biggest sides in the competition. The outcome of the finals is a clear indication that Inter was facing serious problems before the match.