Boss Jurgen Klopp denied disrespecting the FA Cup after much-changed Liverpool were dumped out by Wolves.
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.
He said: "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.
"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."
Jimenez scored seven minutes before half-time when Diogo Jota robbed Milner on the halfway line.
Neves netted from 25 yards just four minutes after Origi's smart leveller as Wolves progressed, the second time in three seasons they have knocked Liverpool out.
Wolves deserved victory just over two weeks after losing 2-0 to the Reds in the Premier League.
Boss Nuno Espirito Santo said of Neves' long-range strike: "It's something Ruben does and we encourage him to do. Last season we saw it often and we know he has this talent.
"It was a very important moment for us and the fans. We'd just lost a goal and to react with such a beautiful goal, Molineux came alive again.
"It was a good performance, it was a tough game. We were organised and had good counter-attacks.
"In the second half the reaction was important but almost immediately we got back on the front foot so, in general, it was a very good performance.
"We go game after game, now we have Manchester City and we've done well against them in the past."