Leading scorer Icardi, who earlier this month extended his Inter contract to 2021, was greeted by several insulting banners on Sunday with fans calling him a "clown" as he took to the pitch for their Serie A game at home to Cagliari.
He then missed a first-half penalty as Inter lost 2-1.
"On another day Icardi would have scored from the spot. I don't want to discuss the rest of it," Dutchman De Boer told reporters.
"We will assess things tomorrow out of respect for the fans and the player. We must find a solution, because the situation is far from ideal."
Local media said some 40 Inter fans had attacked his vehicle after the game and a banner had been hung outside his apartment.
The Argentine had painted the ultras in a bad light with comments in his recent autobiography. They in turn said he was lying regarding an incident in 2015 and demanded he hand back the captain's armband as he did not deserve to lead the team.
UNHAPPY ULTRAS
After a 3-1 away defeat by Sassuolo in February 2015, several Inter players tossed their shirts into the crowd, only to see them thrown back by fans unhappy at their performance.
Icardi did the same, saying he gave his shirt to a young child in the crowd who was immediately told by one of the ultra leaders to hand it back to the player.
The striker then verbally attacked the ultra, saying he was being arrogant in front of children and using them to show how tough he was. Icardi added that his team mates then hailed him "as a hero" for standing up to the hardcore fans.
Icardi had tried to defuse the situation before Sunday's game with a post on social media expressing his support for the club and fans but Inter vice president Javier Zanetti said the player's initial comments in his book had been unacceptable.
"We cannot accept this kind of behaviour from an employee. Will we be taking action? Unfortunately yes," Zanetti said.
"The fans are the most important element, they accompany us and we all should respect them."
The 23-year-old Icardi, who has scored six goals in eight league appearances this season, joined Inter in 2013 from rivals Sampdoria and became captain two years later at the age of 22.
Inter are 11th on 11 points in Serie A.
(Reporting by Karolos Grohmann; editing by Ken Ferris)
