The Hoops saw their hopes of making the next round dashed on Tuesday night as they were beaten 3-0 at home by the Italians.
Despite the loss, Lustig concedes that the Scottish champions did not have that "something extra" to get the result that they needed.
"We played pretty well, had most of the ball and created chances," he is quoted as saying by Sky Sports News. "But it's typical, we haven't conceded a goal from a set play for almost two years and now we've done it twice in one game.
"I don't think Milan created that many chances but to win games at this level you need something extra."
Celtic are back in action on Sunday when they travel to Hearts in the fourth round of the Scottish Cup.