The Reds came from behind to secure a passage to the fourth round of the Capital One Cup thanks to a brace from Nuri Sahin.
And Rodgers believes the nature of his team's victory reflects how much they have grown as a side since their opening day defeat to Steve Clarke's men.
"I think it was a symbolic night because it shows how fast we are moving as a group," Rodgers told a post-match press conference.
"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.
"But the performance level has been high for a number of weeks. I think it's always exciting to see young players who have great technique. But what is important as well is that they understand how to fight. It was a wonderful performance against a good team.
"Steve has done a wonderful job here. He has made the team very hard to beat and obviously tonight he fielded an experienced team. For us to dominate the game like we did and to get the goals, and especially the second goal, it typified what we are all about.
"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 manager was full of praise for Sahin, whose leadership from the middle of the park and instinct to net both Liverpool's goals secured the Reds' progression in the competition.
"He's still getting up to speed," admitted the manager. "It's been difficult for him because he was out for a long time and he's come here having missed a big part of preseason. But he's getting better.
"He has great football arrogance — he's terrific on the ball. You can see in his first goal that he has got great technique and he is not frightened to shoot. And for the second goal, he showed that he can arrive in the box and get a goal."
Sahin's brace means that Rodgers can now relish the prospect of a meeting against former club Swansea at Anfield in late October and naturally, the manager was delighted with Wednesday night's draw.
"Swansea is a wonderful club," he enthused. "I was in no rush to leave there; I was only going to leave there to go to another special club. It will be a great night. To play Swansea at Anfield in front of two wonderful sets of supporters will be a really good night.
"I said to the players afterwards, 'the Carling Cup is stored at Anfield, and I don't want us to give it up too easily.' I want us to fight. You saw tonight that if the young players are fighting and the likes of Jamie Carragher, at 34 years of age, who was fantastic tonight, are performing then we can do well."
With 10 minutes of the game remaining, Jerome Sinclair became the youngest Liverpool player ever when he took to the field to replace Samed Yesil.
And Rodgers revealed how the youngster's work to fulfil his footballing potential starts tomorrow after a memorable evening which culminated in a touching ovation from his teammates following the final whistle.
"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."
The Liverpool supporters were in full voice at The Hawthorns and they voiced their support for the manager by chanting 'One Brendan Rodgers' just moments before Sahin clinched the side's equaliser.
And their fervent support continued right up until the Turkey international sealed a memorable victory.
"The fans have been brilliant for me," insisted Rodgers. "Liverpool supporters are very educated and clever. The support they have given the team and, more importantly myself, has been incredible since the first day I came here.
"This is one of the most iconic clubs in world football but we're not at that level as a team and it's going to take a wee bit of time to build and create an identity that gets us up to that level. When you fight for your life as a manager and players, supporters usually respond to that."
Photo via Liverpoolfc.com