They seemed on track for another three points when Federico Dimarco fired them into an early lead with a fine free-kick.
But Sampdoria leveled in innocuous circumstances as Maya Yoshida’s tame goalbound effort was deflected in off Edin Dzeko.
Lautaro Martinez restored Inter’s lead with a classy finish from Nicolo Barella’s ball, but Sampdoria equalized in the 47th minute from Tommaso Augello.
Inzaghi had started Martinez following international duty with Argentina while Joaquin Correa and Arturo Vidal started from the bench after traveling back and forth from South America.
“I don’t think the problems today were linked to the international break because we conceded two lucky goals and when we were at our best and more space opened up, we carved out three incredible chances with Perisic, Calhanoglu and Lautaro,” Inzaghi said.
“We could’ve retaken the lead, but the injury to (Stefano) Sensi made the last 25 minutes tough.”
On his South American players, he added: “Lautaro, Vidal and Correa all managed to train yesterday, unlike Vecino, and I felt Lautaro had recovered faster than the others. Sanchez only trained with us for three days and couldn’t start.”
Sensi had been a second-half substitute but injured his knee late on, with Inzaghi fearing the worst.
“Stefano’s knee injury is a big shame and unfortunately, we fear well lose him for a while,” he said. Hell have to be assessed and well see.”
Elsewhere on Sunday, Jose Mourinho’s AS Roma won 2-1 over Sassuolo after Stephen El Shaarway’s late winner.
AC Milan won 2-0 over Lazio, Genoa triumphed 3-2 at Cagliari, Udinese beat Spezia 1-0 away and Torino thrashed Salernitana 4-0.