The 27-year-old came on at half-time before being taken off 33 minutes later during his Barcelona debut as they beat Vissel Kobe 3-1.
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Speaking to the press after the game, Flick admitted that Rashford is behind his new teammates and the coaching staff "want to look after".
Flick said: "He’s (Rashford) a week behind the others. He hasn’t been training as much with the ball, and we want to look after him.
“It was a very good match, a good test for us. The first 30 minutes were fantastic. After that we lost a bit of control, but the second half was also very good. I’m pleased.
“What they do with the ball, how they pressed us, it’s really interesting. You can tell they have a clear idea, and it’s similar to ours."