Inter extended their lead at the Serie A summit to 10 points but could only draw 1-1 with Spezia following another Samir Handanovic error on Wednesday.
In their first match since joining and withdrawing from the much-criticised European Super League project, league leaders Inter failed to fully capitalise on second-place Milan's 2-1 loss to Sassuolo earlier in the day.
After scoring an own goal in the 1-1 draw that ended Inter's 11-game winning run in Serie A at Napoli on Sunday, some more shoddy goalkeeping from Handanovic enabled Diego Farias to put Spezia in front early on at Stadio Alberto Picco.
Ivan Perisic bundled in the equaliser on his 200th appearance in all competitions for Inter, who saw Romelu Lukaku and Lautaro Martinez each denied by the offside flag late on as they failed to find the winner that would have boosted their Scudetto hopes further.
Spezia were without their top scorer M'Bala Nzola but managed to take a surprise lead in the 12th minute when Farias' effort from just outside the box squirmed past Handanovic.
Inter's final pass was often lacking but after Nicolo Barella sliced their best opportunity wide, Achraf Hakimi teed up fellow wing-back Perisic for the equaliser ahead of half-time.
The Nerazzurri were buoyed by the goal and Martinez saw his shot come back off the post before being gathered by Spezia goalkeeper Ivan Provedel.
A woeful back pass from Ardijan Ismajli gifted Lukaku a chance to put Inter in front after the hour mark but he was unable to round Provedel cleanly and the keeper recovered well to block his second attempt.
Milan Skriniar was unable to turn substitute Alexis Sanchez's free-kick home before Martinez rattled the upright again in the 80th minute.
Lukaku and Martinez were frustrated by offside decisions, but it looked like the winner was finally about to arrive when the pair combined in stoppage time. However, the Argentina international lashed his effort straight at Provedel.