Luis Suarez completed a superb hat-trick before strike partner Daniel Sturridge rounded off a memorable encounter with a sumptuous 77th-minute lob.
But Rodgers pointed toward an excellent foundation provided by holding midfielder Lucas, captain Steven Gerrard and Jordan Henderson and credited them with making his 3-5-2 formation tick.
|10/3||Luis Suarez is 10/3 with bet365 to be the Premier League top scorer|
"Lucas came in and filled that really well and was excellent in his performance, as were Jordan Henderson and Steven. They made good forward runs and were always available for the ball."
Gerrard and Henderson were among numerous football names to draw withering assessments from Sir Alex Ferguson in the former Manchester United manager's second autobiography, released prior to the weekend.
Sir Alex claimed England captain Gerrard is "not a top, top player", while suggesting Henderson's running style may make him susceptible to injury later in his career.
Rodgers expressed his displeasure at the remarks in his pre-match press conference but denied he used them as a motivational tactic for the pair in the dressing room.
He said: "No, I didn't need to mention it at all.
"As I said, he's a top young player - Jordan Henderson was outstanding today, athletically he was very good, pressed the ball well and he's getting better all the time tactically."
On Gerrard, Rodgers wryly added: "Steven is a top, top, top, top player."