Woodburn scored Liverpool’s second goal in their EFL Cup match against Leeds United, after finishing well from close range.
The 17-year-old has broken Michael Owen’s record to become Liverpool’s youngster ever goalscorer.
However, Klopp was keen to keep the prospect’s feet on the ground after the match.
“First of all, I said ‘Well done, but it was not too difficult! I would have scored too if I would have been in the situation!,” the German boss said.
“Nothing we say here is important enough that it would help Ben Woodburn or myself. It’s all good. We know how to handle the situation and I know I can say to you whatever I want, [but] if he scores goals then it’s quite difficult to stay cool from your side. No problem.
Woodburn’s goal ensured that Liverpool beat Leeds to progress to the semi-finals of the EFL Cup.
Leeds had given Klopp’s side a tough test, but when Divock Origi found the back of the net in the 76th minute, Liverpool always looked likely to make it through.
Woodburn made sure that the closing stages of the contest were a lot less nerve-wracking than they might have been, and the joy in the youngster’s face after he scored was plain to see.
Liverpool will find out who they play in the semi-final later this evening, when the draw is made.