January signing Carroll scored the first of a brace when he fired in an unstoppable strike from the edge of the area after 13 minutes.

The England striker added his second on 35 minutes, just a minute after Dirk Kuyt netted, to leave the Anfield fans singing his name.

"It's been a great day for us, getting my first goal and a great result all round," Carroll told Sky Sports 1.

"The reception I've got from the fans has been great, it's been fantastic since I got here."

Of his first goal he added: "It dropped nicely for me on the edge of the area and I knew I'd hit it (cleanly), and I hit it sweeter than thought.

"We when out to put pressure on them and that's what we did and got goals early.

Kuyt praised the strike pairing of Carroll and Luis Suarez, who have impressed in partnership after the England man had been sidelined for an extended period with a thigh injury.

"The players have been very happy with signings of Andy and Luis," he said.

"Andy's scored his first goals today - it has been tough for him after injury, but he's played very well.

"No-one is more happy than Andy, but his team-mates are happy for him too.

"He's very good in air and can score with feet - he's a big threat."

Manchester City boss Roberto Mancini took the blame for his side's defeat, although he was not willing to divulge why.

"Tonight I made a mistake, it was my fault," he said.

"I think the players can do better, but I made a mistake.

"I know (what the mistake was). It is for me.

"I am sorry for the fans. We only started to play after 20 minutes."

Mancini's night was soured further with star striker Carlos Tevez forced off after just 16 minutes with a hamstring injury.

The Italian manager admitted Tevez would struggle to be fit for the weekend FA Cup semi-final with Manchester United at Wembley.

"His hamstring is very difficult for Saturday.

"It is very diff as it is only five days away.

"We'll try (to get him fit) but we probably need two weeks."

Liverpool boss Kenny Dalglish was pleased for his new striker Carroll and expected the former Newcastle man to flourish after breaking his Reds duck.

"The first goal was a great strike and second was a great ball in and a good flick on," he said.

"That won't do him any harm to score his first goals at Anfield."

He added: "I think it is a gratifying performance for everyone.

"I thought we thoroughly deserved victory. The way we went about our work was a great credit to ourselves and the football club."

"We could have scored before we did. They're very honest lads and have worked very hard since I've come in."