The Liverpool manager's former club took more compensation for his summer departure to Anfield as they knocked the holders out of the League Cup to a chorus of: "We don't need you any more."
Luis Suárez gave Liverpool belated hope at two goals down with a glancing header from Steven Gerrard's free-kick but it was not enough to prevent Michael Laudrup's team reaching the quarter-finals for the first time in Swansea's history. They survived a nervous, desperate finale with Suárez going close once more but the quality of their play on the counter- attack had troubled Liverpool throughout.
Swansea brought an impressive following from south Wales and Laudrup, who would have joined Liverpool in 1983 but for a contract dispute that enabled Juventus to acquire his exquisite talent, showed similar intent towards the competition by naming a side containing seven of the players who started at Manchester City. One notable absentee was the goalkeeper Michael Vorm, and Swansea could miss his influence for eight weeks after he damaged a groin in Saturday's 1-0 defeat.
Rodgers could make no such demands of his regulars having played a near full-strength team against Anzhi Makhachkala in the Europa League three days before the Merseyside derby. He opted for nine changes from the Everton starting lineup and an Anfield debut for Samed Yesil, the promising 18-year-old striker signed for £1m from Bayer Leverkusen in the summer. Joe Allen also faced his boyhood club for the first time since his £15m departure from the Liberty Stadium and made a lively start. Unfortunately for the spectacle, he was in a minority.
Jordan Henderson and Stewart Downing, two of the more experienced and certainly expensive members of the Liverpool team, showed an immediate rapport down the right but the home side rarely threatened Vorm's replacement, Gerhard Tremmel, in the Swansea goal. The cup tie ambled on for 25 minutes with the feel and bite of a testimonial. But then the visitors – inspired by Miguel Michu at centre-forward – took control through a fine exhibition of one-touch passing and intelligent movement.
The Spaniard served notice of the problems to come for Liverpool when he combined well with compatriot Pablo Hernández inside the home penalty area. Hernández had a clear sight of Brad Jones's goal but cut inside Sebastián Coates on to his right foot. The moment's delay allowed Jamie Carragher to roll back the years and throw himself in the way of a goal-bound shot. But Swansea's pressure was unrelenting for 10 minutes.
Michu almost capitalised on a Coates' back-pass only for Jones to intercept neatly. The 26-year-old then dispossessed Allen deep inside the Swansea half, with what appeared a foul, and sent Nathan Dyer sprinting clear behind Henderson at right-back. Dyer squared to Jonathan de Guzmán but just as the Swansea hordes prepared to celebrate a superb counter attack, the Canadian put too much weight on his chip over Jones to send the ball wastefully over. He then received a mouthful from Michu for not passing to the unmarked forward. In fairness De Guzmán did have only the keeper to beat.
Ki Sung-yeung forced a low save from Jones with a 25-yard shot and the lead that Swansea had long threatened arrived from the resulting corner. Dyer swung the delivery out from the right and Chico Flores, the visiting central defender, powered in ahead of Coates to divert an unstoppable header wide of the Liverpool goalkeeper.
Liverpool, who had tested Tremmel only once before falling behind through a Downing effort, should have levelled seconds later when Oussama Assaidi's left-wing cross picked out Joe Cole unmarked in front of goal. From only six yards, however, the former England international sent a feeble header straight at Tremmel.
The miss was the only impression made by Cole on his first start since August and his place in Rodgers' affections was demonstrated at the interval when both he and Yesil were withdrawn. Liverpool's manager had seen enough, and perhaps heard enough of his former supporters christening his team a second-rate Swansea, to bring on the insurance policy of Suárez and Steven Gerrard after 45 minutes.
Their arrival prompted a more urgent display from the entire Liverpool team, and a long overdue one at that. Moments after the restart Allen capitalised on a defensive slip and picked out Jonjo Shelvey inside the area. The midfielder made space for the shot with a good first touch but blazed over from 16 yards. Shelvey turned provider with a cross from the left that Suárez headed off target at full stretch, and the Uruguay international also shot over from the edge of the box. Liverpool's attempts were all going the same way but at least they had arrived. Gerrard struck a post from 25 yards courtesy of a slight touch from Tremmel in the Swansea goal. The rebound went hard and straight at Downing who prodded wide.
As with the first half Swansea took a while to find their rhythm up front but it was cutting when it came. The visitors queued up to double their edge when Hernández broke free on the left and forced a save from Jones at close range. The Australian international blocked the rebound, and another from Michu, before the forward teed up Dyer and Carragher ran to the rescue once more.
Jones also saved well from Michu on the turn, Ashley Williams headed wide from the resulting corner and Dyer did apply the cushion of a second goal as Michu and Hernández led a devastating break. Hernández rolled the ball across Jones for Dyer to convert into an empty net. In the closing stages, De Guzmán made the game safe in stoppage time with an almost identical finish to Swansea's second goal. The outstanding Michu broke clear down the left and rolled the ball perfectly across the Liverpool goal for the midfielder to slide home.