Champion's League is completely different from the local leagues. Have you seen how Inter Milan's performance has been in the Seria A? They are number 7 according to the current standings with 5 wins and 4 losses out of 9 games. But they did manage to beat Barcelona that hasn't lost a single local league game so far.
You cannot play in the Champions League the same way you did in your home league since it is the league of champions. Due to the numerous benefits and recognition that come from the competition, every team takes it extremely seriously and strives to perform better. I must say that when Milan defeated Barcelona, I wasn't shocked. For us, this is the constant fun and nature of the champions league.