Bournemouth boss Marco Rose refused to blame England for the injury which will keep Alex Scott out for a number of weeks.
The Cherries are understood to be unhappy that midfielder Scott played in the 7-0 win in Croatia despite feeling discomfort in his thigh beforehand.
"It's an injury from a muscle, and we'll do pictures [scans] in some days again," said Rose at a news conference.
"But we're going to miss him, for sure, for four or five weeks. I'm very disappointed and it's a big loss.
"Did he have an injury before? No, I think not. I think the club already said everything about it.
"For me, it's disappointing. We miss a very important player, but I don't want to blame anyone. We are very happy that he made his debut for the English national team.
"He did well and we just hope that he is getting fit again quite soon."
Bournemouth face Chelsea this weekend as the Premier League returns after the international break, where Scott made a full England debut in Croatia.
England boss Thomas Tuchel said about Scott after the Croatia win: "First start and what a start, what a performance.
"He is so smooth on the ball, his decision making is at the highest level.
"He plays with so much confidence. He is so active, so confident. The work rate off the ball.
"He is just the complete package. He gave us a lot of mobility and a lot of variety and work rate in the centre of the pitch."
But Scott withdrew from the squad who went on to beat Czechia due to injury.
Tuchel said: "With Alex, it's a bit of strange one. I'm very sad about it.
"Alex trained both training sessions before the match full against Croatia. He did extra work after the training sessions.
"We knew that he was in treatment, but there were only green lights from himself, from the medics.
"When we asked him, when we were aware that there is a slight discomfort throughout the match, we asked him if he wants to come off. He said no.
"After the match, he said like, 'yeah, OK, it was the right thing to do, but I could have played 90 minutes, I don't feel an injury' and even on the day after here before we did the scan, he felt that he's not injured, so it's a strange one because it does not match the objectivity of the scan and the prediction of the time that he is obviously going to miss.
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"It doesn't match his feelings and doesn't match at all the process into the match and during the match.
"There was zero risk-taking from our side. There was no awareness that there is any risk of something could happen like this. It's a kind of a one-off, strange one.
"I can 100% understand that Bournemouth is not happy and sad because they lose a key player."
Press Association contributed to this report.