Woodburn, who has previously represented Wales at youth level, was promoted to the senior squad by Coleman ahead of their World Cup qualifier against Ireland on Friday.
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."
Read the full article on eurosport.co.uk: Klopp did not get call from Coleman over Woodburn call-up