First half strikes from Ante Rebic and Ibrahimovic himself had Milan believing they could upset their tile chasing neighbours.
However, a second half collapse saw Marcelo Brozovic and Matias Vecino draw Inter level less than ten minutes after the restart, before Stefan de Vrij and Romelu Lukaku rounded off a 4-2 win, leaving Zlatan furious.
Speaking to Sky Sport Italia after the game, he said: “It's difficult to explain what happened. At half-time we told ourselves the first 15 minutes going back out there will be crucial, and in that 15-minute spell we conceded two goals.
“We stopped playing, the team stopped believing, we stopped pressing, didn't pass it around enough. From the equaliser onwards, everything collapsed.
“I think a lot of it is down to experience, because you must know how to control a game at 2-0 up, not just winning at the end.
“It’s strange because our first half was practically perfect. I expected more from Inter and the first half performance did not look like a team worthy of second place. They did after the break.”
The forward’s frustrations were echoed by his manager Stefano Pioli, who said the performance made him ‘angry’.
“The first half was born from the strategy studied during the week, in the second half there were two episodes where we had to do much better,” he said.
“We were strong in the game, the two goals changed the game. Then we had the chance to equalise, but in those first two goals our carelessness weighed. We penalised an important performance.
“The games change and we had to be much more careful, Inter are much more experienced than us and used to playing certain games. They also had a bit of luck, we hit two posts.
“I was angry with the players because we had defensive tasks. It was the best performance, we put a strong opponent under pressure who had 19 more points.
“With more attention we would now be here to talk about a different game. We had a great game, it is absolutely the best first half of the season.”
The result means Inter stay top of the Serie A table, ahead of Juventus on goal difference and just one point above Lazio.