As had been the case on Wednesday at Anfield, the Reds bounced back from a goal down to lead 2-1 as the game in the Potteries entered its final 20 minutes.
This time, however, Klopp's men avoided the concession of a late equaliser to claim a crucial three points in their push for Champions League qualification.
Speaking after the match, the manager expressed delight over the improvement he had witnessed in such a short period, and commended the squad's refusal to give up in the face of adversity.
"We already did better after being 2-1 up in the last game, so we used the experience of that," he said.
"We didn't play these long balls without a target, one or two of them were there because that's how it is.
"The difference could not be bigger between a 2-1 win and a 2-2 draw at home. In the last game against Bournemouth, it was pretty similar. 1-0 down, 2-1 up, 2-2. Big difference.
"We don't have the most comfortable situation at the moment, it's not like we fly or something because of the results we have, or we can always use the last game to be confident.
"We really appreciate the boys fight for each point, it's not about being genius.
"We have a few injuries, a few players missing here, ill there, little bit injured here. It's really difficult but nobody waits for us, it's not like we can ask to play a week later until it's better.
"That's why it's so important for us, I only want to see everybody can see we really fight for the Champions League.
"Will we be there at the end of the season? No-one knows. But we will try to be one of them."