Marcus Thuram struck twice - and had another deflected into the net - with Nicolo Barella also scoring.
“The lads did very well, especially the opening half-hour, then it was inevitable we’d sit a bit deeper towards the end,” Inzaghi told DAZN.
“Beating Atalanta like this is very satisfying. I saw four days of very intense training and today it all paid off, so I congratulate the players.”
“Let us not forget we were up against a very good team. The lads showed great concentration, we allowed Atalanta very little.”
On two-goal Thuram, Inzaghi also said: “Thuram is starting to get more experience in Serie A and is building on last season. It all starts from his mentality and his hunger, he returned to the training ground early from vacation because he knew that we needed him.
“The strikers are all doing well, I liked Taremi and Arnautovic when they came on too. We’ve got to keep the bar high and we did.”