The Swans left Michu and captain Ashley Williams on the bench - with one eye on next weekend's Capital One Cup final against Bradford - and were punished as goals from Philippe Coutinho, Jose Enrique and Luis Suarez were sandwiched by Steven Gerrard and Daniel Sturridge penalties.
"It was an important three points," said Rodgers.
"We've had a bumpy road this week in terms of games Monday and Thursday (2-0 defeats to West Brom and Zenit St Petersburg) but the Premier League is very important for us and we knew we had to show focus and determination.
"I think we showed character and mental toughness to get a result like that.
"There obviously was a part (of the cup final) 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."