Adrien Rabiot and Nicolo Fagioli scored in the second half to give Juventus the win, although Inter were the better team for the first 45 half.
"It's a painful defeat in a big match against our competitor. This is football, perhaps last season we beat them without deserving it and clearly tonight, 2-0 is an unfair result," Inzaghi told DAZN.
"Unfortunately, these matches are decided by incidents and we didn’t manage to get them our way, so we have to do better."
Inter had 14 shots on goal in the game, with both Lautaro Martinez and Denzel Dumfries missing clear opportunities in the first half.
"That is where the regrets are. We started the second half well too, hitting the crossbar with (Hakan) Calhanoglu and then conceding on the counter-attack. We lost our unity a little, still had the chances to equalise and then conceded again," Inzaghi said.
"At this moment, Inter must focus on becoming more consistent. We were coming off four consecutive victories, we are back on the field in a couple of days and a defeat like this can leave some psychological scars, as it was an important match."
Inter host Bologna on Wednesday before playing Atalanta on November 13th in the last game before the World Cup break.
