Brendan Rodgers revealed his bemusement at criticism of Raheem Sterling after his man of the match display fired Liverpool into the Capital One Cup semi-finals.

The 20-year-old shone in the 'false nine' position against Championship leaders Bournemouth and netted either side of Lazar Markovic's first goal for the Reds as they teed up a two-legged semi against Chelsea.

Sterling made the trip to the south coast on the back of a 22-match goal drought which stretched back to September, having found David De Gea in world class form in Sunday's 3-0 defeat to Manchester United.

His manager questioned why the attacker, who continues to be linked with a move to Real Madrid as he is yet to sign a new deal at Anfield, has come under fire in recent weeks.

Rodgers said: "I thought he was outstanding. The kid, for some reason, seems to be getting a lot of stick off a lot of people for something.

"His contract situation is absolutely nothing to do with him and his representatives are working with the club.

"He is, as you can see, happy and enjoying his football. At Old Trafford he was unfortunate not to score and in that role he plays you think of Alexis Sanchez when he plays for Arsenal.

"He is not an out-and-out striker but his speed in front of the back four and behind them causes problems and you've seen that with him here, he can get it, turn and go at defenders.

"He has been like that all season and been a real catalyst for us."

Sterling ended a stunning passing move with a close-range header to break the deadlock and he put the game beyond the Cherries with a textbook run and low finish.

The England winger should really have taken home the matchball but dragged an effort wide after being superbly teed up by Adam Lallana, one of a number of chances squandered by a revitalized Liverpool.

And Rodgers saw plenty in the opening hour to suggest the worst weeks are behind his struggling side.

"It was an outstanding performance," he said. "I can certainly see signs that we are getting back to where we were. There is a long way to go but this was a tough game, coming to a side top of the Championship.

"They are going well and for us to come and dominate like we did and score the goals that we did was very pleasing."

While Eddie Howe admitted the technical quality of Liverpool in the first half proved to be too much for this table-toppers he was bemused by the unusual circumstances of Liverpool's second goal.

Cherries captain Tommy Elphick mistook a whistle from the crowd for referee Mark Clattenburg's and stopped as Philippe Coutinho went to shoot at Artur Boruc's goal.

The ball fell to Markovic, who doubled Liverpool's lead – and in the midst of the celebrations Elphick was seen pointing at his ears to explain the error.

"I don't know what to say on that, I have never really seen that before," Howe said.

"I haven't had a long conversation with the players, I am aware Tommy stopped because the thought the referee had blown.

"I heard the whistle myself from the stand. It's a bizarre one and Tommy has obviously genuinely believed it to be the referee's – but there you go.

"I'm sure the person who has done it wouldn't have meant it to have cost us a goal."

Despite being 3-0 down after 51 minutes Bournemouth rallied and after Dan Gosling squeezed in a consolation the former Everton midfielder rattled a post to leave Howe with some encouragement.

"We showed great character in the second half, dug in and came out all the stronger for it," Howe added.

"And if the second one from Dan Gosling had gone in it could have been a nervy finish."