Rodgers' men were on the back foot early in Monday's Premier League clash at the Liberty Stadium as Liverpool struggled to cope with Swansea, in the starting 3-4-3 formation.
However, after switching to a diamond in midfield, the visitors improved and took maximum points in the hunt for a top-four finish courtesy of a deflected Jordan Henderson strike 22 minutes from time.
"In the second half we were outstanding, but the first half [was] nowhere near the level we would expect," Rodgers told Sky Sports.
"3-4-3 is a complex system and there's not been too many times it's not worked, but in the first half it didn't work well.
"We gave it away too cheaply. We then changed the midfield for the second half and I thought we dominated second half.
"We were much better with possession and looked like we could score more than one. We had an outstanding mentality and it's another three points.
"The attitude and energy has to be important. We weren't on it for whatever reason but give credit to Swansea, they played well.
"The enthusiasm to press the game was much better [in the second half] and we created better options."
Henderson's winner extends Liverpool's unbeaten league run to 13 matches, with Rodgers' side having not conceded away from home in the top flight since mid-December.
"We know we can go away from home and win because of the character and resilience of the team," he added as his side continued to make amends for their woeful start to the campaign.
"To come away, get a clean sheet, six in a row [away from home], and another victory is a great effort.
"From where we were, the intent to give us a fighting chance...[the players deserve] monumental praise, but we haven't done anything yet."
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