Klopp believes Woodburn's selection has come too early with the player only making his first start for Liverpool in January.
"Actually, I was surprised about this. I don't know exactly how it's normal here," the German told British media.
"This should not be a criticism, but usually when you call up a player, a 17-year-old player, I thought it would be possible to call me.
"He has to learn, he has to develop, he has to improve, all of this... there are now two managers responsible for him."
Coleman, whose Welsh side are currently third in Group D of the UEFA zone qualifying stage, said Woodburn was ready to take a step forward in his international career.
"If I thought it was too early for him I wouldn't have called him up, because this game is massive for us," Coleman told the reporters.
"I am thinking about what is the best squad to get together to meet this next challenge. And Ben has done enough."
The winners of the nine European groups will progress to the 2018 World Cup in Russia, while the eight best runners-up enter a regional playoff round to compete for UEFA's remaining four places.
(Reporting by Hardik Vyas in Bengaluru)