Reds manager Brendan Rodgers said that the Denmark international's problem "doesn't look good" after the match and also revealed that forward Fabio Borini has a swollen ankle
The Danish defender suffered the problem after a clash of legs with Antonio Valencia in the lead up to United's second goal, which was dispatched by Robin van Persie from the penalty spot following Glen Johnson's fouling of the Ecuador international.
The Dutchman was forced to wait to take the penalty as Agger was treated by physios, and was eventually taken off the pitch on a stretcher and replaced by Jamie Carragher.
Liverpool manager Brendan Rodgers revealed after the match that the Reds' medical team suspect that the Dane has suffered a medial ligament problem, and also confirmed that Fabio Borini had a swollen ankle.
"Fabio had a badly swollen ankle," he told reporters. "Agger's doesn't look good, the medics were saying it might be a medial ligament. We'll see."