Coleman said he expected Wenger to hand Ramsey an extended break following the tournament in France.
"It's disappointing he's got an injury. Could it have been prevented? Possibly, yes," Coleman told reporters on Wednesday.
"I think we all expected him to (miss the start of the season), so I don't know what happened between and when he ended up on the pitch.
"I think, to a man, if you were looking at that (team sheet against Liverpool), it was a bit of a surprise he started.
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"I think Aaron said himself (in France) that he wasn't expecting to."
Defender Laurent Koscielny, midfielder Mesut Ozil and striker Olivier Giroud were all left out of the team for the game against Liverpool.
"It was a long tournament for Aaron, after a long, hard season. So I don't know why he was treated differently," Coleman added. "I think Arsenal have a certain way of doing things.
"A lot has been said about their injury list, they're doing the same things now as what they've always done - they're not going to change now.
"That's up to them, Aaron's Arsenal's player."
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
