The Argentina international scored a 90th-minute penalty to secure a 1-0 win for the Milan-based side, the second match in succession that an Icardi spot-kick has proved decisive for Inter after Sunday's 1-0 success over Cesena.
Some fans voiced their disapproval with Inter's struggle to break down previously unbeaten Sampdoria during the game by booing and whistling.
Icardi stressed his appreciation to those that back the club, but stated that those who whistle the team are not true supporters.
"We don't feel the criticism," Icardi told the Gazzetta dello Sport. "We go out on to the pitch to win, and we have to continue like this.
"Those who whistle do not love Inter. But there are also those who support us for 90 minutes, those are the real fans."
Icardi previously played for Sampdoria between 2011 and 2013, but he insisted that the goal against his former side was no more important than any other.
"No [it is no better scoring against Sampdoria], it's the same as scoring against other teams, although they launched my career," he added.
"It was important for the team, and we continue on the road we started against Cesena.
"We have a game every two days, and we have to work very hard."