Lautaro Martinez struck a hat-trick on the night, with teen Giacomo De Peri making his debut.
“I am very satisfied and congratulated the lads, because our journey over these eight games has been extraordinary,” Inzaghi told Sky Italia.
“We kept seven clean sheets, we only finished outside of the top 3 due to goal difference. We have this consistency and you just need to see the names of some of the teams who failed to make the top eight, so we need to celebrate deservedly achieving this.
“The lads had the right approach, as we knew Monaco had these dangerous counter-attacking players, so we had to be very organised. Even a defeat might’ve seen us qualify, but we tried not to make any calculations and just go for the victory.”
He continued: “In the last 12-13 matches, I always tried to alternate. I had left a few players out at Lecce who I knew would come in handy here, such as Barella, Dimarco and Pavard, while for the others I had to make certain choices.
“They were all ready, we gave a debut to a youngster late on too and that shows how well the Inter youth academy is working.”