The victory, which made it 17 goals scored and just two conceded in five home matches which have brought 12 points, moved the Reds back up to seventh in the Barclays Premier League table but still nine points adrift of fourth-placed Tottenham having played one match more.
However, Rodgers, conscious that his positive outlook is often used as a negative against him, admits there is plenty of work still to do in the remaining 11 matches.
"I am an optimist, you have to be, but we'll not get too carried away," he said.
"I've likened us to a marathon runner just getting ready for the finish line, ready to make our move, and then we trip ourselves up.
"That is something we have to change going forward for the remainder of the season and finish as strong as we can."
The slip-ups came earlier in the week as having lost 2-0 to West Brom, ending a run of three successive Anfield victories, they also lost by the same scoreline to Zenit St Petersburg in the Europa League.
But with Swansea manager Michael Laudrup doing his predecessor a favour by naming an understrength side as he looks to Sunday's Capital One Cup final Liverpool were able to take advantage.
Steven Gerrard opened the scoring with a first-half penalty, making up for the spot-kick he failed with against the Baggies with the game still goalless, before a brilliant burst just after half-time secured the result.
Within 16 seconds of the restart £8.5million January signing Philippe Coutinho, on his full debut, made it 2-0 and within 10 minutes Jose Enrique and Luis Suarez had doubled that advantage.
It was only left to Daniel Sturridge, generously handed the duties by Gerrard, to convert Liverpool's second penalty of the afternoon and Swansea were dispatched with consummate ease.
"It was an important three points," said Rodgers.
"We've had a bumpy road in terms of games Monday and Thursday but the Premier League is very important for us and we knew we had to show focus and determination.
"I don't think you can take anything away from the Liverpool players but it (the final) was something Swansea were thinking about."