Inter Milan's faint title hopes grew even thinner as the loss left them 18 points behind runaway league leaders Napoli.
Riccardo Orsolini's 76th minute strike condemned the Nerazzurri to their seventh defeat of the season.
Four days after recording a 1-0 win over FC Porto in the first leg of their Champions League round of 16 tie, Inzaghi was left to bemoan his side's lack of consistency.
"There will be a lot of talk about the defeat and there will be criticism, but I'm the coach and I'm primarily responsible," he said.
"We have to say that even if the result had been different, we couldn't have been happy with our first half.
"We have to analyse and understand why these drops happen to us after the European matches, we have to do more and better."
"If you go to watch matches, after the Champions League we often have some problems.
"Then away from San Siro the problem becomes even more pronounced and we have to try to do better.
"Today's first half was insufficient, the second was better, but in the moment in which we had created the conditions to win the game, we conceded goals."
