Ciro Immobile inspired an admirable recovery from a half-time deficit as the visitors broke Juve's remarkable 57-match unbeaten run at home in all competitions.
The win also saw Lazio move level with the champions on 19 points, five shy of early pacesetters Napoli.
"It is only right that people talk about Lazio as we achieved something remarkable this evening," Inzaghi told Mediaset Premium.
"The lads deserve credit for a result that will go down in the history of the club.
"I did get the feeling we could hurt Juve if we just hung in there. Some people said we would be in ninth or 10th place this season, which is unfair, so now it is only right that people talk about us."
Lazio's two goals each arrived within 10 minutes of the restart as Immobile came back to haunt his former club with a match-turning brace.
Inzaghi insists he was always confident in the team's ability to respond to Douglas Costa's opener.
"I said to the lads at half-time that we could have done better in the final third and just had to work on that final ball," he said.
"We were doing okay, but to win we needed to give something more, have clear heads and play without pressure.
"In the second half we felt freer, we were doing the moves that we had worked on in training.
"It is never easy with the fans and atmosphere in Turin, as there is a reason they have not lost here in almost three years."