Simone Inzaghi was left anguished after his first Serie A defeat as Inter boss came at his former club Lazio, admitting: "We lost our heads."
A 3-1 setback came after a flurry of second-half goals from the home side in Rome, with the defending champions knocked out of their stride late on by a moment of controversy.
With Inter's Federico Dimarco down, apparently injured, Lazio played on and got the 81st-minute goal that put them 2-1 ahead, Felipe Anderson netting from close range after Ciro Immobile's strike was parried by Samir Handanovic.
Inter were furious and both sides had two players booked as bickering on the pitch threatened to spill over. Sergej Milinkovic-Savic sealed the points in stoppage time with a fine header, ending Inter's seven-game unbeaten start to the league campaign.
Inzaghi's new team took the lead against his former charges when Ivan Perisic converted an early penalty, but Lazio had a spot-kick in the 64th minute after Patric's header from a corner was handled by Alessandro Bastoni. Immobile tucked away that chance and the comeback gathered momentum from there.
The result rankled with Inzaghi, who said afterwards: "That was our best recent performance, but when a team like ours is a goal up, we have to manage the game better in terms of our final ball and double our lead."
Quoted on the official Inter website, he added: "Unfortunately, they scored their equaliser from a corner that we shouldn't have conceded. From that point on, the game changed and Lazio got back into the contest.
"The second goal was a bit strange and we lost our heads, which is something we can't allow to happen. It's disappointing. It's a setback that we didn't need in terms of our league position, but we'll take the performance and move on."
Inter sit third in the Serie A standings, behind Napoli and Milan, and their next league clash sees them face Juventus on Sunday of next weekend.
"When you face sides like Lazio, you can't give them a chance to get back into the match," Inzaghi said. "We managed the contest particularly well for an hour, but we then let our opponents back into the game and paid the consequences."
1 - Ivan #Perisic is the first Serie A player to score a right-footed penalty goal and to score a left-footed penalty goal since 2004/05 (since Opta collected this kind of data). Ambidextrous.#LazioInter pic.twitter.com/dByGRuLeoE— OptaPaolo (@OptaPaolo) October 16, 2021
Lazio head coach Maurizio Sarri said Inter should have put the ball out of play themselves when they had an opportunity after Dimarco went to ground.
Sarri was also dismayed to see Luiz Felipe, who had an excellent game in central defence, red-carded after the final whistle.
Luiz Felipe, in celebration mode, jumped on his former Lazio team-mate Joaquin Correa, who left for Inter in August. Correa did not see the funny side and Luiz Felipe was in tears after being dismissed.
"Luiz Felipe told me he was saying goodbye to Correa, they played together for a long time. They didn't want to fight," said Sarri. "It's a big misunderstanding."