Simone Inzaghi blamed an Inter "blackout" for the 3-2 derby defeat to Milan at San Siro as Rafael Leao's double settled the Derby della Madonnina.
The Inter head coach was unimpressed with his team's defensive performance as the Rossoneri took local bragging rights, with Leao's double and an Olivier Giroud strike countered by goals from Marcelo Brozovic and Edin Dzeko.
Inzaghi, whose title hopefuls have lost two of their first five games of the Serie A season, praised Milan goalkeeper Mike Maignan, although the Frenchman only made three saves.
"We found a great Maignan and they scored against us very easily," said Inzaghi. "To win the derby we needed to do more, half an hour is not enough."
Brozovic gave Inter an early lead, but Leao levelled in the 28th minute, on his 100th Serie A appearance.
The Portuguese winger set up Giroud to put Milan ahead, before dancing through a ragged Inter defence to fire the nominal home side 3-1 ahead, at the stadium the clubs share.
Dzeko halved the deficit, but Inter could not get back on level terms.
"Now we will analyse the game and our mistakes," Inzaghi told DAZN. "At the beginning the game was balanced. After the 1-1 we had a blackout half an hour which cost us two goals that we cannot concede. We probably deserved more, but we had to do better."
He added: "I have to try to understand what happens to us in those moments: we are the same as last year, but we have conceded eight goals in five games."
Milan boss Stefano Pioli saw his side go at least briefly to the top of the table.
"There is a great rivalry that has strengthened in recent years," Pioli said of the derby. "Inter wanted to prove themselves superior, but they did not succeed. I coach lads who continue to amaze me with their energy and their constant desire to improve.
"We were good at reading the game, Inter made us dribble and we did it without forcing hasty plays.
"We had prepared for the game in this way, precisely knowing how Inter would play. We have shown maturity on the pitch, we have an awareness that makes me happy. For 70 minutes we played like a great team."
Pioli's lone complaint was that he felt Milan let their attention drift after going two goals clear, saying that at that point, "we thought we had already won, and it is a mistake we must not make".