A hat-trick from Marcus Thuram secured a 3-2 home victory, with Torino struggling with ten men after an early sending off for Guillermo Maripan.
Inter have won three matches in a row in all competitions and are second in Serie A but Inzaghi was not happy with his team's showing on Saturday.
"Clearly, we need to improve in some aspects, we pay a heavy price for every tiny distraction," he said.
"We worked really hard on details that need to be whittled down, the lads have great spirit, but considering everything we did today, today's game shouldn't have ended 3-2.
"Seeing a team perform like this in three matches makes me want to congratulate these guys. We need to keep working the way we are, and in our penalty area, we all need to be more attentive."
Inzaghi admitted that Inter have an issue with closing out matches, as Torino managed to remain on the offensive late in the game despite being a man down.
"We're working on it, and we need to do more. Over the past two days, the team has trained extremely well, and we're trying to pay even more attention to the finer details," he said.
Inter will travel to AS Roma on October 20th following the international break.
