Woodburn, aged 17 years and 45 days, beat Michael Owen's club record by 98 days after an emphatic 81st-minute finish in the 2-0 win over Leeds in Tuesday night's EFL Cup quarter-final at Anfield.
He had only made his first-team debut in Saturday's victory over Sunderland - and that was barely a minute at the end of the match - but he is highly rated within the club and the fact he was born in Chester, like Owen, will only lend itself to unrealistic comparisons at such an early stage.
Woodburn, a 67th-minute substitute, grabbed all the headlines in a match which the visitors dominated for over an hour before Divock Origi's second in as many matches broke the deadlock in the 76th minute.
"We know how to handle the situation," said Klopp, whose side booked a record 17th League Cup semi-final, and their fourth in the last six years, having lost the final to Manchester City last season.
"I can say whatever I want but if he scores goals it's difficult to stay cool from your (media) side, no problem. But nothing what we say here is important enough to help Ben Woodburn or myself.
"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 press)."