Inzaghi's side lost the final 1-0 after a second-half goal from Rodri, but the 47-year-old Inzaghi remained upbeat after a tough season in which he came under heavy pressure before guiding his side to third place in Serie A as well as winning the Italian Cup and Super Cup.
"On a night like this, I can't single players out who played below par. I said yesterday I would not change my players for anyone else, and tonight the world saw why," Inzaghi told Sky Sports Italia.
"They showed the whole world how well they stood up to Manchester City, a side that everyone knows has so much quality.
"I hugged my players one by one, as they were extraordinary, just as our fans were and deserved a different result, but I hope they were happy seeing the way the team played tonight."
Inzaghi has faced harsh criticism from fans and media.
"Both I and my players were attacked and admittedly we lost some games that we shouldn't have lost, but I think we learned valuable lessons from those defeats," he said, pointing out that the team had won four trophies over the last two years.
"With this spirit, organisation and determination, I think we will be back here again in future," he added.