Their 2-2 draw with Bayern Munich at San Siro saw Inter win their quarterfinal tie 4-3 on aggregate.
Inzaghi remarked afterwards: "These are nights that will stay with us. We had to play two great games and we did them, it was wonderful. You will find opponents of great calibre but I am lucky to have great men.
“It was very important, and that’s why I say that the difference in the new Champions League is in this, in the two extra games. And that’s why, compared to last year, we had a few more problems.
"For the rest, the Champions League doesn’t forgive anything. You have to have great intensity. The lads were very good, between the first and second legs we played two great games."
Asked directly what is the secret of his success as Inter coach, Inzaghi was adamant.
He insisted: “How good the boys are tonight. It was enough to see (Joaquin) Correa, (Piotr) Zielinski and (Denzel) Dumfries tonight who seemed as if they were on the bench with us.
"They all help each other, they know that by playing so much they are all useful to the cause and they are ready."
Inzaghi concluded: "It's clarity, tonight we were clear-headed in the difficult moment. Tonight after the blow to (Henrikh) Mkhitaryan we thought the game could have stopped and instead we conceded the goal.
"At that moment a team not clear-headed could have gone off track, instead we always remained focused and clear-headed, continuing with the game plan."