Just three days prior, Woodburn made his first-team debut in the dying seconds of Liverpool's 2-0 victory over Sunderland on home turf.
Klopp is keen to help develop the teenager and fellow academy players, but is concerned about the media's role.
"It's all good. We know what Ben's capable of," Sky Sports News quotes Klopp as saying. "My first job is to help these boys be the best. There's a lot of things to do, especially to keep the public away as long as possible. That's quite a difficult thing to do.
"But we only bring him when we want to use him. That means when he is on the pitch, he is absolutely allowed to score goals. I am really happy with him, the only problem is I am a little afraid about you (the media).
"We know how to handle the situation. I can say whatever I want but if he scores goals, it's difficult to stay cool from your side, no problem. Nothing what we say here is important enough to help Ben Woodburn or myself."