A 12th-minute own goal from Joseph Yobo and Dirk Kuyt's close-range effort 10 minutes from time flattered the visitors, who were second best for most of the game.

However, considering the inconsistent start to the season, which was compounded by Wednesday's failure to qualify for the Champions League group stages, Benitez was keen to accentuate the positives as the Reds moved up to fifth in the Barclays Premier League.

"I think it was really important for us. We won against Debrecen (in midweek) and we knew we had to keep winning," said the Spaniard.

"A derby is always very difficult and also very important so a win today could set us up for the rest of the season.

"We are higher in table now, everyone is happy, so we will see if we can keep winning some games."

Merseyside derbies are always fiercely contested but the fact Liverpool were on the back foot for so long was a tribute to the work-rate and drive of Everton.

Benitez accepted his side had to soak up the pressure but, boosted by the early goal, they at least had something to hang on to.

"It was a clearly a difficult game from the beginning. They were playing a direct and also a set-pieces game," said the Liverpool boss.

"It was very difficult to control that because they are strong in the air but we showed character and were trying to play counter-attack - sometimes with good possession, sometimes not so good.

"They were on top of us but we showed character, we won and scored two goals and at the end of the game maybe we had better control."

Benitez also hailed an "amazing" double-save from goalkeeper Jose Reina 20 minutes from time when, with his side under pressure, the Spain international dived low to his left to keep out Tim Cahill's header and then stood up to block Marouane Fellaini's rebound.

"It was a great save from Pepe Reina, which was crucial also. He showed he is a top-class keeper," said Benitez.

"To defend a lot of throw-ins, corners and free-kicks during 90 minutes against a team which is good in the air as Everton is not easy but he helped the team and in this situation he was amazing."

Everton invited actor Henry Winkler, who famously played television's the Fonz and is currently in pantomime in Liverpool, to today's match but even he could not bring Happy Days back to Goodison Park.

Toffees manager David Moyes felt his side did not deserve to be beaten but admitted Yobo's failure to clear Kuyt's cross in the build-up to the second goal cost them a chance of getting anything from the game.

"I don't feel we came off the pitch losers today. The players worked extremely hard and they I felt they deserved more than what they got in the end," he said.

"The deflected goal took the sting out of us. I don't know how many times Liverpool had been in our half up to that point but it wasn't many.

"But I thought the players reacted great. They kept going and I thought in the main we kept Liverpool quiet.

"The game was tight and we, in the main, were trying to set the tone and make it difficult for them.

"It is disappointing you don't get anything from that.

"I think the two saves by Reina [were crucial]. I felt maybe our luck would change in the second half and we would get the goal but maybe that double save just altered it a little bit.

"But up until it went to 2-0 I can't remember Liverpool having a chance apart from Emiliano Insua's first-half header.

"But in big games especially you hope you don't get situations where there are mistakes because it is hard enough to score a goal without making anything which leads to one."

On-loan Manchester City striker Jo, making his first start for more than a month, had the ball in the net twice in the first half but was flagged offside on both occasions.

Moyes had no issue with the decisions and was happy with the Brazilian's performance in the 65 minutes he was on before being replaced by Louis Saha.

"I thought Jo did really well and I also think the linesman got them (the offside decisions) both correct."

The defeat, which extends Everton's current run to one win in the last 11 matches, leaves the club three points outside the relegation zone.

Despite an improved performance against their near-neighbours Moyes knows his side have to improve.

"Overall I thought the players did a good job. I've got encouragement from today but it doesn't change our position," he added.