A young Reds team fell behind early on, as Gabriel Tamas capitalised on a Brad Jones error, but grabbed the win through midfielder Nuri Sahin's double and the manager believes that the victory was a fitting illustration of how far his team have come since suffering a 3-0 defeat against the Baggies on the Premier League's opening day.
"I think it was a symbolic night because it shows how fast we are moving as a group," Rodgers told reporters.
"How we have progressed from our first day of the season here, when we were a wee bit disjointed and players did perhaps not quite understand my methods and what I wanted.
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"Overall, the confidence on the ball and the ability to pass it and the courage to want it was very prominent with the players.
"It's really been the last three or four weeks when our tempo and rhythm and relentless possession has started to come through, so it was good to see and it was good to win."
The 39-year-old handed Jerome Sinclair a substitute appearance which made him the club's youngest-ever player at the age of just 16 years and six days but the former Swansea City boss warns that the forward must now build on his 10-minute cameo in order to become a fixture in the first team.
"I gave him my congratulations," said Rodgers. "He got a nice round of applause afterwards in the changing room as well.
"It was nice that Jack Robinson was the previous [holder of that record] and he was playing tonight. But now Jerome's hard work begins. It's no good being the youngest player and then drifting out of it.
"But thankfully, he's a good kid. I've worked with him a number of times so far and he's really focused with good concentration. He wants to learn and once you have that hunger, you can take it a long way."