The 38-year-old, who returned to the club in December on a free transfer, had earlier inspired the Rossoneri into a 2-0 half-time lead at San Siro.
Another new arrival, Ante Rebic, had put Milan in front before Ibrahimovic doubled the advantage, and at that point Inter looked set to miss the chance to leapfrog Juventus at the Serie A summit.
However, Antonio Conte’s side hit back in the second half, with goals from Marcelo Brozovic, Matias Vecino, Stefan de Vrij and Romelu Lukaku completing the fightback.
And after the game, Ibrahimovic was not best pleased.
“It’s difficult to explain what happened,” the frustrated Swede told Sky Sport Italia.
“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.”
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Milan came into the clash having lost just once in their last 11 fixtures.
But with just 32 points from 23 matches, they lie a disappointing tenth in the table.
And Ibrahimovic has urged the squad to become more street-smart following the setback.
He added: “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.”
Milan will hope to bounce back when they host Juventus in Thursday’s Coppa Italia semi-final first leg tie.
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