The German midfielder marked his debut with a 17th-minute headed goal from David Accam's cross to get the Fire off to a flying start.
But two goals form the Impact, a red card to each side, and a late leveller from Luis Solignac forced the draw at Toyota Park.
"It was a great feeling," Schweinsteiger said after the match.
"Perfect cross from David and the header [on the goal].
"It was a good feeling at first, but I'm a little bit sad and not so happy that we couldn't win the game."
Fire head coach Veljko Paunovic added: "I think [Schweinsteiger] was great.
"To start the debut with a goal, it's always something that we all dream of. Opening the game as we did with his goal was an important thing for our team.
"On his game, we improved obviously; with his quality passes in the final third, smoothness in the build-up and calm, we were more patient with the ball and that helped the team, especially in the first half.
"We have to work, obviously to give him the best possible support and recovery and prepare him throughout the whole season, but we are very happy with his performance."