The Reds boss opted to start the two teenagers with Philippe Coutinho and Roberto Firmino deemed too unfit to start, while the visitors were also missing key players such as Sadio Mané, Jordan Henderson and Adam Lallana in the Potteries.
But Klopp's bold decision to entrust the club's youth in an unfamiliar 3-5-2 formation left Liverpool second-best to the Potters in the first-half, trailing 1-0 at half-time from a Jonathan Walters header.
Only when Coutinho and Firmino were introduced did Klopp's charges spring into life, both producing strong saves from Lee Grant after they replaced Alexander-Arnold and Woodburn at the break.
Within two minutes, Coutinho brought Liverpool level before Firmino struck to fire the Reds in front as they went on to claim a huge three points in the race for Champions League qualification.
Asked whether he was worried about the effect of withdrawing Alexander-Arnold and Woodburn so early on their confidence, Klopp said: Yeah usually I would be but we have such a close relationship.
We didn't utilise youngsters, insists Klopp
"All the boys went in the dressing room and didn't celebrate. The boys didn't look like it's the best day in their lives. Maybe it started like this and it doesn't end like this, that's life.
"They don't have to react like adults, they're disappointed but we will help them more than we help anybody else so everything is fine. It is not about them. We didn't use them, they weren't involved in the game. They only had two or three situations.
"How I said, if it is a penalty - which I thought it is - then Ben does his job because he was in a situation in the box where obviously the opponent cannot win the challenge without making a foul. We could have scored and everything would have been fantastic. It's not their job to be the best players on the pitch.
"They are outstanding talents, they are fantastic boys, our boys, so everything will be good, yes. It didn't feel like I want to do it [take them off] more, each week or something like this, it's not nice, but it's the job."
"Coutinho and Firmino were only fit enough to have lasted 30 minutes if they'd started"
Quizzed as to whether super-subs Coutinho and Firmino could have started the game, such was their impact from the bench, Klopp added: "It was like, as we understood it, the possibility was pretty high that we would have to change one of them after 30 minutes.
"We have a lot of numbers, different things what we get from sports science and everything. This was the moment when each alarm clock was ringing, if you want, for both of them.
"You saw it I thought in the second-half. Brilliant brilliant but then half-an-hour, really difficult. It was not a plan to change twice at half-time but if you start them, we would still have to.
"It was with offensive options it was difficult, for Daniel [Sturridge] half-time is really long in the moment in an intense game like this so it was difficult to find the right solution.
"Maybe lucky at the end that it worked out but I thought a lot about it and even when nobody really understands it, that was my decision. I found the solution.
"I thought we could have played much better than we did but it was clear that we want to bring them, half-an-hour absolutely makes sense and if it is then 0-0, they can decide the game. They had to do a little bit more work."