Boss: We're showing signs of improvement

The Reds rediscovered much of their rhythm on a night when Raheem Sterling spearheaded the team's attack and his pace and instinct was supplemented by star turns from the likes of Philippe Coutinho and Lazar Markovic.

Sterling latched onto Jordan Henderson's cushioned header to open the scoring at the Goldsands Stadium in the quarter-final before Markovic clinched his first goal for the club with a composed finish from the edge of the penalty area.

For the third, Sterling raced through the Bournemouth defence after the interval to fire beyond Artur Boruc - and while Dan Gosling struck one back for the home side, Rodgers was able to reflect on a confident display and an important win for his charges.

"It was a tough game coming here," Rodgers told reporters at his post-match press conference. "I know the Championship well enough and I know Eddie [Howe] well enough to know that he produces good footballing teams.

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"They are a team that has been working very well. So for us to come and dominate and score the goals we did was very pleasing.

"Despite the result at Old Trafford, I saw moments in our game that I thought were good [against Manchester United]. We created a lot of chances, so I can certainly see signs of us getting back to where we were. We know there's a way to go.

"I think slowly we're getting there. I've said that my teams have shown here at Liverpool that as the season goes on they get better and better. There are a lot of players adapting.

"You saw young Markovic tonight - he gave an outstanding performance. I'm looking to find solutions to make us more creative, because we haven't been that at all this season and that's the mark of the team.

"We obviously work very hard on our possession and movement and creativity. It's taken a long time for us to find rhythm this season. But what has never stopped is the work-rate of the players. You come to places like this tonight and it takes character and quality to get through.

"I thought the first goal was a wonderful example of our patience, movement and creativity. It was an outstanding goal. We showed real authority on the ball and we waited for the moment to penetrate a very good team."

The Reds moved the ball around with patience and composure in the build-up to their first strike of the game before Markovic seized control to float a cross towards Henderson, who set up Sterling for the opener.

"That moment of the game required patience and that was good," reflected Rodgers. "Tactically, the players were very good. They had to be patient. Bournemouth are a very good side. They are well drilled and well organised, closing the gaps.

"So we had to move the ball from side to side in order to penetrate. That patience is what is required. There are other times when we break away and someone will dribble and go through and score. But I thought overall it was an outstanding team performance and the goals were great to see."

Sterling operated in a central attacking role against the Cherries and the youngster thrived on the night, dropping deep to link the play and pull players out of position, as well as breaking through the Bournemouth ranks with his pace.

"He's enjoying his football," said Rodgers. "At Old Trafford he was unfortunate not to score but he was a real threat. I think you saw him tonight in that role. You think of Alexis Sanchez when he plays for Arsenal in that position.

"He's not an out-and-out striker. His speed and movement in front of the back four and behind them causes problems. You saw that with Raheem tonight - his ability to drop in, turn and go at defenders.

"You see his threat on the counter-attack and his link-up play. I thought he was outstanding tonight. He has been a real catalyst for us this season."

Liverpool were cruising at 3-0; however, Bournemouth refused to relent in the game and when former Everton midfielder Gosling controlled the ball in the box before spinning to apply a finish beyond Brad Jones, the Reds were forced to focus.

"We've got to first of all stop the cross and then it's a mistake in the box, which allows them to get the goal," said Rodgers. "It doesn't matter what the score is, they get a little bit of momentum from that.

"We spoke about that at half-time and we said that there would come a stage at some point where we'd have to stay compact and stay together.

"They had a wee spell where they hit the post but I thought we recovered well and got our composure back again. We were relaxed on the ball and we saw the game through, created some more chances. We could have been more comfortable, but I'm happy we scored three."

Following the final whistle on the south coast, Liverpool discovered their fate for the final four of the competition as the draw paired the Reds with rivals Chelsea, who they will host on January 19 before making the trip to Stamford Bridge on January 26.

"Our objective tonight was to go through and we knew whichever team we got [in the semi-finals] was going to be a difficult game," said Rodgers. "You have to beat the best teams in the competition - whether it's the semi-final or the final. It's over two legs and we'll really relish that opportunity."

The manager opted to withdraw Dejan Lovren at the half-time interval, replacing him with Mamadou Sakho - and Rodgers explained the substitution was brought about by a groin problem the Croatian sustained during the opening 45 minutes.

"We'll just see and assess him tomorrow," said the boss. "He had a wee nick in his groin. So we'll see how that is."