The Bianconeri had gone behind after 19 seconds in Turin, but fought back for a 3-2 victory.
"When the fixture list was drawn up, everyone said we'd have a really tough start. I'd have been more than happy with six wins and a draw by this stage," Conte told Sky Sport Italia.
"It was a good performance tonight, but we have to improve. At the moment we concede with the first shot on target, so that's bad luck but also our own mistakes. We have been living with this situation for a while; it's almost as if we need a slap to wake us up...
"Today was crazy, as I almost didn't notice Milan had scored after 20 seconds. We did well to get back on our feet against a strong Milan."
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