Ruben Neves' thunderbolt sealed a 2-1 third-round win for the hosts after Divock Origi had hauled Liverpool level.
Raul Jimenez opened the scoring after James Milner's first-half error and Wolves travel to Stoke or Shrewsbury in the fourth round.
Klopp made nine changes, including handing Curtis Jones and Rafael Camacho their debuts, while defender Ki-Jana Hoever became the club's third youngest player ever.
He replaced Dejan Lovren, who suffered a hamstring injury after just five minutes to increase Liverpool's defensive injury issues.
Klopp outlined he was forced into most of his changes and insisted he did not disrespect the cup.
"I'm not sure what you all would have said if our centre-half situation (from the start) was Fabinho and Ki-Jana, probably a few smart people would have told me I don't respect the competition," he said.
"It doesn't make sense to bring a 16-year-old boy from the start but he came on and did well. I changed a lot because we have to, not because I wanted to.
"After the City game we had immediately a few players who were ill with a sore throat. Pretty much all the players who weren't here today had little problems.
"Adam Lallana and Jordan Henderson were in our plans. Dejan was not in our plans, he was only supposed to be on the bench. The intensity of the last few games gave me information it is not possible to start with the three up front.
"We have been playing with a similar line-up in some really tough games."