The 22-year-old forward – who has come under scrutiny for failing to reproduce the prolific form which earned him a big-money move from Newcastle – netted his first league goal of the season to give Dalglish’s men the lead in the 71st minute before Luis SuÃ¡rez made the points safe eight minutes from time.
Dalglish, however, believes the media has made too much of Carroll’s form since he arrived on Merseyside in January and claimed his hefty price-tag is “irrelevant”.
“I think the problem with Andy Carroll is the media, yourselves,” he said after the game. “You keep talking about his way of life, and you don’t know what that is.
“In training he’s fine. The price is irrelevant. He’s every bit as important to us as Steven Gerrard and [Jamie] Carragher who never cost us anything. He never had anything to prove; we’re delighted for him.”
Everton were reduced to 10 men in the 23rd minute when referee Martin Atkinson showed Jack Rodwell a straight red card for what appeared to be a fair challenge on SuÃ¡rez.
Tim Howard then ensured the home side went in level at the break when the Everton goalkeeper saved Dirk Kuyt’s 44th-minute penalty after Phil Jagielka brought down SuÃ¡rez in the box.
But Carroll got the crucial breakthrough for the visitors when he smashed home Jose Enrique’s cross after 71 minutes. And man-of-the-match SuÃ¡rez then snatched his fifth goal of the season when he capitalised on Sylvain Distin’s failed clearance.
“Until they lost a man it was even,” said Dalglish, whose side move up to fourth in the Premier League table. “[Tim] Cahill had a header and Pepe [Reina] made a great save.
“There wasn’t much between the teams. Sometimes the numerical advantage works in your favour, sometimes it goes against you. It was hot out there, and we kept moving the ball and kept our patience.
“I haven’t seen it [the sending off] and I don’t intend to either.”
Meanwhile, Everton boss David Moyes claimed the referee’s decision to show Rodwell the first red card of his career “ruined” the encounter.
“I thought the decision just ruined the game,” said Moyes. “Thereâ€™s a lot of questions that people ask in the media about the derbies and the tackles and the sendings off prior to games – but that wasnâ€™t down to a bad tackle by a player today.”
Everton: Howard, Hibbert (Vellios 78), Baines, Jagielka, Distin, Coleman (Drenthe 59), Cahill, Osman (Neville 69), Fellaini, Rodwell, Saha.
Liverpool: Reina, Jose Enrique, Carragher, Kelly, Skrtel, Downing (Bellamy 67), Lucas (Henderson 88), Adam (Gerrard 67), SuÃ¡rez, Carroll, Kuyt.
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