Icardi, who was replaced as club captain by Samir Handanovic this week amid speculation surrounding his future, watched from the stands at San Siro due to the knee injury that kept him out of the 1-0 win over Rapid Vienna on Thursday.
Inter chief executive Giuseppe Marotta confirmed before kick-off the Argentina striker would still be offered a new contract despite the seemingly strained relationship between player and club.
Spalletti's side struggled in front of goal and needed a winner from Radja Nainggolan after Manolo Gabbiadini cancelled out Danilo D'Ambrosio's 73rd-minute opener.
While the Inter boss was pleased to see Icardi, who did not travel to Austria with the team, in the stadium, he was disappointed he did not come down to the dressing room afterwards.
"I really appreciated that he was in the stadium and I would've appreciated it even more if he had come to the dressing room to celebrate with us afterwards, because it was a very important victory for the team and he is part of this group, so I imagine he was as happy with the win as we were," said Spalletti.
"We want a return to normality. In a team, in a dressing room you all need to be working in the same direction.
"There are more steps to take, which are for him to come to the dressing room, to enjoy being a part of this very good group, to relish wearing Inter's glorious shirt."
Spalletti fell out with club icon Francesco Totti at Roma but stated the situation with Icardi is unprecedented in his career.
"I really liked the applause from our fans after the equaliser, as they urged us to get right back on track and gave us strength in that difficult moment," he said.
"It's just frustrating that we keep getting tied up in all this talk around Inter. I've had some situations in my career with a lot of attention, but never like this.
"The victory is a sign of maturity, so we can begin to get past the mountain of things that are constantly spoken about Inter."