The former Germany international made the move in March, having been frozen out by Jose Mourinho at Old Trafford.
But the 32-year-old has been less than impressed with the quality on show in America, with his side on a three-match winless run.
"Chicago Fire finished as the bottom club in the previous two seasons and I did not expect that we'd win every match and finish on top by a mile," Schweinsteiger told Suddeutsche Zeitung.
"One player's influence in football is not as big as in other sports, it's 11 players vs. 11 players. And we didn't play all that bad until now and were pretty much on [the same] level in our losses to Toronto and New York Red Bulls. But we still have a lot of work to do.
"We all know that this league is just not like the Premier League or the Bundesliga and, of course, it can be frustrating on the pitch at times when things discussed [in the team meeting] are not implemented or when somebody loses a ball or just does not have an eye for the teammate.
"I don't blame anyone for it, that's my problem – I need to adapt to the league and cope with those situations.
"If you compare it to Bayern Munich or the national team, the difference is huge, but I knew what I let myself in for."
Unfortunately no win today. The team played very well in the first half and we are looking forward to the next match against Seattle. https://t.co/akGXar8AYK— Basti Schweinsteiger (@BSchweinsteiger) May 7, 2017
Schweinsteiger has won the World Cup, Champions League and eight Bundesliga titles during a glittering career in which he has become accustomed to playing alongside extremely talented players, but he knows he is in a different world now.
The former Bayern Munich midfielder added: "The league is interesting because it's evident everyone can beat everyone and sometimes things happen you just don't understand. This might be referee decisions or the running paths or passes of a teammate.
"It's different than in Europe, but you have to take things as they are.
"Not everything is seen that happens on the pitch -– the teammate in a good position, where it might get dangerous, how a situation develops. Too many balls are lost as well. But that's normal.
"If this were not the case, the people would not play in the United States but rather in the Bundesliga, Premier League or La Liga. Still, MLS has potential, a lot of potential."
Schweinsteiger has scored twice in six MLS appearances, helping the Fire to sixth place in the table.