A 12th-minute own goal from Joseph Yobo and Dirk Kuyt'sclose-range effort 10 minutes from time flattered the visitors, whowere second best for most of the game.
However, considering the inconsistent start to the season, whichwas compounded by Wednesday's failure to qualify for the ChampionsLeague group stages, Benitez was keen to accentuate the positives asthe Reds moved up to fifth in the Barclays Premier League.
Mersey-pride: Javier Mascherano shoots for goal.
Enlarge .the ball deflects off Joseph (not pictured) and past Tim Howard.
Enlarge .and the Argentine celebrates with team-mates Dan Agger (left) and Lucas (right)
"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 factLiverpool were on the back foot for so long was a tribute to thework-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 wereplaying a direct and also a set-pieces game," said the Liverpool boss.
"It was very difficult to control that because they are strong inthe 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 scoredtwo goals and at the end of the game maybe we had better control."
Flying: Dirk Kuyt celebrates after scoring the clincher
Benitez also hailed an "amazing" double-save from goalkeeper JoseReina 20 minutes from time when, with his side under pressure, theSpain international dived low to his left to keep out Tim Cahill'sheader 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.
Fonz's approval: Actor Henry Winkler enjoys the match
"To defend a lot of throw-ins, corners and free-kicks during 90minutes against a team which is good in the air as Everton is not easybut 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 bebeaten but admitted Yobo's failure to clear Kuyt's cross in thebuild-up to the second goal cost them a chance of getting anything fromthe game.
"I don't feel we came off the pitch losers today. The playersworked extremely hard and they I felt they deserved more than what theygot in the end," he said.
"The deflected goal took the sting out of us. I don't know howmany times Liverpool had been in our half up to that point but itwasn't many.
"But I thought the players reacted great. They kept going and I thought in the main we kept Liverpool quiet.
Hey Jo: Everton's Brazilian striker wraps his long left leg around the ball
"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 .125were crucial.375. I felt maybeour luck would change in the second half and we would get the goal butmaybe that double save just altered it a little bit.
Having a ball: Liverpool keeper Pepe Reina removes a beach ball from the pitch
"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 situationswhere there are mistakes because it is hard enough to score a goalwithout making anything which leads to one."
On-loan Manchester City striker Jo, making his first start formore than a month, had the ball in the net twice in the first half butwas flagged offside on both occasions.
Moyes had no issue with the decisions and was happy with theBrazilian's performance in the 65 minutes he was on before beingreplaced 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 thelast 11 matches, leaves the club three points outside the relegationzone.
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.
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