Schweinsteiger came on as a second half substitute replacing Michael Carrick in the final third of the game against Tottenham.
The 30-year-old Germany international admitted his surprise at the support he received from fans during his league debut.
"It was amazing, really," he told MUTV. "I was surprised and I have to say 'thank you' to all the supporters.
"It was a great feeling and yes, at the end, we won so it was a good day for us.
"I’d played twice before in the Champions League but this was something new on Saturday.
"The support is huge; I knew that before I came here and saw it in the USA as we had a lot of supporters there too. It was great and a special day for me on Saturday."
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Bastian Schweinsteiger has thanked fans for their reception during Man United's clash against Spurs
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