Steven Gerrard, Philippe Coutinho, Jose Enrique, Luis Suarez and Daniel Sturridge were all on target as the Reds replaced the Swans in seventh position on the table and Rodgers was delighted to return to winning form after losses to West Bromwich Albion and Zenit St Petersburg even though their opponents had other things on their minds.
"I think we showed character and mental toughness to get a result like that," he told Sky Sports.
"There obviously was a part (of the Capital One Cup final next weekend) in it.
"They were still a strong side and they will be disappointed with the performance but if you don't have Ashley Williams or Michu, who has been brilliant since he came in, then that can affect your team.
"I don't think you can take anything away from the Liverpool players but it (the final) was something they were thinking about next week.''