A 2-1 second-leg triumph saw Inter win the round 16 tie 4-1 on aggregate. Marcus Thuram and Hakan Calhanoglu struck Inter's goals.
Inzaghi said: “I’m very happy, getting into the quarters is extraordinary. I feel a few compliments should be given to this team, and I will give them publicly tonight.
“The support of our fans is enough for us, but I would like to hear even more, this team is doing great things, which are often taken for granted. Nothing should be taken for granted in football.”
On his 200th game with Inter in all competitions, Inzaghi also said: "I know what it means to coach Inter - tonight it was my 200th match here. There were so many joys and some disappointments but you try to honour each match in the best way for the good of Inter."
Inter now meet Bayern Munich in the quarterfinals and Inzaghi added: "It will be difficult but we will play the games as we have done so far. I just hope to have everyone available."