The Northern Irishman was given a good reception by the Liberty Stadium faithful but was ultimately left frustrated as the Reds failed to make the most of their opening hour superiority.
The closest Rodger's men came to a goal was Jose Enrique's close-range first-half effort from a delicate Luis Suarez pass but the strike was chalked off for offside.
Rodgers said: "We were unfortunate with the offside goal; that was a goal – I have seen it on the replay.
"But we are now eight games unbeaten and we are chipping away and our method was good today."
Enrique and Glen Johnson also wasted chances for the Reds, while Raheem Sterling hit the bar before he conspired to bungle a two against one situation with Suarez.
Rodgers admits his side need to be more clinical as they look to continue to progress.
He said: "We need that little bit of quality in the final third. That's something we will look to improve on.
"But I was pleased with our creativity and method and we were just a bit unfortunate with the offside goal and the chance we had with the two on one.
"It looked like he played the pass too early and Raheem then gave him a ball that knocked him wide on the return.
"We would hope to be more clinical but that is experience, he is only 17."
Rodgers praised the home support for the greeting he received.
He said: "It was an emotional return. I will always remember my time here with good memories."