The Nerazzurri took a two-goal lead after 12 minutes at the San Siro, but Mazzarri believes that his players took their foot off the pedal for Raphael Martinho's 31st-minute strike.
"We started really very well and once we got to 2-0 up, we started to show off and play more for the crowd than to get goals - we shouldn't do that," the 52-year-old told Sky Sport Italia.
"We lost concentration and conceded a goal, so we could've done ourselves even more damage and in future we'll pay for that attitude.
"This is a team with many young players. As long as everyone was concentrated and did their part, we played a fantastic game. I told the lads that until we learn these lessons, we cannot think of troubling the top teams."
Inter, who are now fourth in Serie A, take on Atalanta on Tuesday.