Trophy treble remains in Pool's sights
Houllier's side may be struggling in the league but have a taste for knock-out competitions. They moved into the fourth round thanks to a 47th-minute penalty converted by midfielder Danny Murphy.
And the win means Liverpool are still in with a chance of a trophy treble as they are also involved in the Worthington Cup and UEFA Cup.
Houllier said: "It was a massive win for us and I am very proud of the attitude of the players. Our club has a tradition of success and of winning trophies. This is an important day.
"We had a plan and we didn't give City too many chances. We showed a lot of solidity and strength.
"This is the second time we have gone to a Premiership club in the cup and won. Don't forget we beat Aston Villa in the Worthington Cup." City striker Nicolas Anelka, who had a spell on loan at Anfield last season, was left frustrated.
Houllier said: "We didn't have a plan to stop Anelka in particular. We looked at the whole team."
The match-winning penalty was awarded by referee Uriah Rennie after Marc-Vivien Foe appeared to handle a cross from Vladimir Smicer.
City manager Kevin Keegan said "technically it probably was a penalty".
However Keegan added: "It was a horrible way to end a cup tie, although we never got going.
While there was a degree of controversy about the spot-kick being awarded, Liverpool were well worth the victory.
City, who have settled in so well to life in the top flight, looked out of sorts in front of their home support.
Houllier made four changes to the side that lost to Newcastle for the third round tie at Maine Road.
Neil Mellor was handed only his second start of the season and partnered El-Hadji Diouf up front. Milan Baros had to settle for a place on the bench while Michael Owen was still ruled out through injury. Murphy after a one-match ban Djimi Traore and Vladimir Smicer were all restored to the starting line-up.
City were without defenders Richard Dunne (virus) and Steve Howey (Achilles). Gerard Wiekens and Lucien Mettomo were drafted in.
Keegan decided to shake things up five minutes before the break. In a bid to bring a bit more creativity to his side he drafted in midfielder Eyal Berkovic for Mettomo. Berkovic had been struggling with a groin strain that forced him to miss the 2-2 draw against Everton on New Year's Day. He released Anelka two minutes before the break but Kirkland stood tall to block his effort.
There was a dramatic start to the second half with Liverpool taking the lead in the 47th minute.
Smicer's intended cross was handled by Marc-Vivien Foe and referee Rennie had no hesitation in awarding a penalty. Murphy, back in the side after a one-match ban, stepped up and sent Schmeichel the wrong way with his spot-kick.
: Schmeichel, Wiekens, Mettomo (Berkovic 41), Distin, Jihai (Goater 70), Benarbia (Huckerby 85), Foe, Horlock, Jensen, Wright-Phillips, Anelka.
: Kirkland, Carragher, Henchoz, Hyypia, Traore, Murphy, Diao, Gerrard, Smicer (Riise 86), Mellor (Heskey 73), Diouf.
Referee: U Rennie (S Yorkshire).
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