Brendan Rodgers oversaw his first Merseyside derby victory as Liverpool manager on Tuesday night - and afterwards dedicated a ruthless 4-0 win to the supporters.

His Reds side were rampant from the very first whistle, harrying Everton into errors and driving forward with a deadly sense of purpose.

Steven Gerrard epitomised Liverpool's hunger when he towered highest in the penalty area, powered a header home and then sprinted to the fans to celebrate in the 21st minute.

Daniel Sturridge was clinical, clipping the second over Tim Howard before improvising from the edge of the area two minutes later to lob the American for 3-0.

Luis Suarez notched an obligatory strike, speeding half the length of the field before calmly rolling home the fourth in front of the Kop.

Reflecting on the Reds' biggest win over their rivals since 1982, Rodgers said: "I'm delighted for the players and obviously the supporters.

"I know that feelings run high here on Merseyside for the derby games. It was a brilliant team performance. There was good defensive organisation. We were outstanding on the counter attack and we controlled our spaces really well.

"We were clinical in front of goal. We scored four and could have had arguably two or three more. It was a brilliant win for us and I'm delighted for everyone.

"It's obviously really special because of the nature of the game - it was two teams that have been doing outstandingly well and doing the city proud throughout the course of the season.

"It was a combination of the players and the supporters - they were brilliant again tonight. I'm delighted for them because I know how special the derby games are here and how special they are for the supporters.

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"For them to get that win and the victory, and for the players to perform how they did, was really special. We've got a real focus and concentration going into every game.

"This was a massive game tonight as everyone who came to the ground knew, so for us to score goals, defend like we did and attack with that efficiency was very pleasing.

"We knew it was going to be a big match. I'm more delighted for the players and supporters. For me, it's three points; I'll be more delighted at the end of the season if we can arrive in the top four. I'll probably overanalyse the performance and see the areas we can improve on going forward."

Rodgers' side could have had more goals during a second half in which they attacked the Kop with constant menace.

Sturridge saw his penalty go over the bar after Raheem Sterling was brought down in the box by Howard - and the Reds carved a host of opportunities to extend their advantage beyond four goals.

"For us, it was a tireless performance," said the manager. "To win the big games like these here, you've got to attack and defend together, and I thought our unit - right the way from the goalkeeper to the front players - worked tirelessly at filling the spaces. Then, when we had the ball, we looked a real threat.

"All wins are important, but especially against your rivals. We know there's still a wee bit to go, but psychologically it was a big, big win for us and one that can reiterate the confidence and belief in the squad.

"We've just got to keep putting our foot to the floor, keep giving these performances and keep scoring goals."

The victory moves the Reds four points clear of their neighbours, who are currently embroiled in the race for a top-four position in the Barclays Premier League.

Rodgers said: "I think we've shown all season that we're going to be in contention for fourth place and we know that there's going to be one or two other teams fighting for it.

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"We've shown a wonderful team spirit here [at Anfield]. We've had various players missing at various times. But we've been able to structure the team so that we're not relying on any one player.

"It's really about the ethos of the team and that was seen tonight. Our attacking players were filling in the spaces and putting the work in."

Rodgers chose to withdraw Sturridge in the 71st minute, introducing Victor Moses in his place - and the boss explained how his decision to substitute the England international was purely a tactical one.

"It wasn't a difficult decision to take him off," said the Northern Irishman. "I thought his two finishes were sublime. He was outstanding in the game.

"He's always a threat. He looks like he can score in every single game that he plays in and he normally does, but I just wanted to shore the game up. We'd put the risk in the game for that first hour or so and we had to balance out on that side.

"Jordan Henderson had to put a real shift in to get across. So it was time, I felt, to make the change and balance the team back up again and then there was no problem.

"As a coach, to get Sturridge and Suarez into the same team, it's a bit of a risk because others have got to fill in. But I'd rather do that to give us that offensive threat.

"Then we have to look to close the door somewhere else with other players in the team. Everyone has to work together and that was important for us tonight."

Gerrard set the ball rolling for a famous victory with a powerful header in the 21st minute. The 33-year-old went on to dominate the game from a deep-lying central position.

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Afterwards, his manager was full of praise for a commanding performance that will rank among the skipper's finest against the Blues.

Rodgers said: "Those of you who have seen him over 31 games in the derby, where has been all action and his influence in these games has been wonderful - he was equally as good tonight, but from that deeper position.

"He has really taken to the role, he understands it and we speak a lot on it. You saw his responsibility in the role, he's organising the team on the field. He scored a goal and is such an unselfish guy, a really generous man.

"A local guy in a derby game, to give away a penalty [to Sturridge], shows the mark of the man he is. He led the team marvellously well and was outstanding."