Ivan Perisic scored an injury-time equaliser as Inter came back from two goals down to draw 2-2 with Parma on Saturday, while Atalanta beat bottom club Crotone to move second in Serie A.
Antonio Conte’s Inter have dropped points in three of their first six league games this season and could slip five points behind city rivals and leaders AC Milan, who visit Udinese on Sunday.
Gian Piero Gasperini’s Atalanta, who drew 2-2 with Ajax in the Champions League in midweek, sit one point behind AC Milan.
Inter dominated the first half at the San Siro, but Perisic volleyed off target and Achraf Hakimi nodded over from close range when he should have done better.
Parma made their hosts pay in the first minute after the break, as Gervinho powered home his first goal of the season.
The home side were given a mountain to climb just after the hour mark when Roberto Inglese slid the ball through for Gervinho to score his second.
Inter were desperate to try and keep pace with AC Milan and got themselves back into the game less than two minutes later thanks to Marcelo Brozovic’s deflected strike.
Andrea Ranocchia almost levelled shortly afterwards, but saw his header saved at point-blank range by Parma goalkeeper Luigi Sepe.
Perisic headed in Aleksandar Kolarov’s free-kick in the second minute of injury time, but it was too late for Inter to find a winner.
Luis Muriel scored twice as Atalanta bounced back from successive losses in Serie A with a 2-1 win at Crotone earlier on Saturday.
Atalanta conceded seven goals in back-to-back defeats by Napoli and Sampdoria.
They were not at their fluent best on Saturday, but did enough to edge out Crotone, who remain without a league win this season.
Gasperini said he had tough decisions to make ahead of next week’s crucial Champions League group-stage game against Liverpool, after Hans Hateboer and Cristian Romero were both substituted at Crotone with muscle problems.
“Serie A and the Champions League are two very different tournaments and I don’t want to choose between them,” he told Sky Sport Italia.
“We’ll have to wait until tomorrow to see, (defender Rafael) Toloi also had a heavy knock to his knee, so we’ll see who we can recover and who we can’t.”
Muriel, who scored 18 Serie A goals last term despite only starting 10 matches, grabbed a 26th-minute opener by collecting Ruslan Malinovsky’s pass and drilling a low shot into the net.
Papu Gomez wasted an excellent chance to double the lead, but Colombian forward Muriel did slot in his second goal seven minutes before half-time.
Nwankwo Simy gave the hosts hope before the break, but their frustrations boiled over in the second half and coach Giovanni Stroppa was sent to the stands after receiving two yellow cards in a matter of minutes.