The 18-year-old Yamal will miss Sunday's LaLiga home game against Valencia and is doubtful for next week's Champions League clash at Newcastle because of the injury, Flick told reporters on Saturday.
"Lamine will not be available tomorrow, it's a pity. He played with the national team despite pain. He had problems, played 79 and 73 minutes, and didn't even train between matches because of this pain," Flick said.
"That is not really taking care of the players, is it? It is not. Spain, they have the best team in the world, best players in the world. In every position, they are unbelievably good. So, maybe they will also want to take care of our players, our young players, but it's like they are doing this (to them).
"This is what I can say and I'm really sad about this."
Yamal, widely regarded as one of Barcelona's and Spain's best players, skipped training on Friday after complaining of discomfort. Flick said he had already been carrying an injury and was given painkillers to play for Spain.
The teenager, who helped Spain to win the Euros last year, played 152 minutes in World Cup qualifiers away to Bulgaria and Turkey last week, contributing three assists.
Flick, who coached Germany before his appointment at Barcelona, said he did not speak to Spain coach Luis de la Fuente about the issue.
"I was also on this side, as a national team coach. I know how hard sometimes the job is," Flick said.
"I never spoke; I have had one conversation via text but I never spoke with him. My Spanish is not good, his English is not good, so maybe this is a problem."
"But in the end, I think the communication - because we have not only one player there, we have many players there - it could be better."
Flick's side will also be without midfielder Frenkie de Jong against Valencia after he was injured while on duty with the Netherlands. Midfielder Marc Bernal, 18, will return after 13 months out with an anterior cruciate ligament injury.
Barcelona's press officer Gabriel Martinez, who accompanied Flick at the media conference, said he was uncertain if Yamal would be available for their Champions League opener at Newcastle.
"Yes, discomfort in his pubic bone. He has been tested. He is doubtful for Newcastle," he said.