The £35 million frontman has thanked everyone who supported him after first league goal of the season at Goodison Park, and wants to build on important win in tough matches to come
Carroll netted the crucial opening goal for Kenny Dalglish’s men with just under 20 minutes remaining to cap a powerful display at Goodison Park.
After a disappointing start to the campaign, the former Newcastle man was keen to thank all those who supported him in difficult times.
"The goal is for everyone really, Kenny [Dalglish], the other lads and the fans. Everyone who has stood by me," he told the club’s official website.
"I had been speaking with Jose [Enrique] and I told him that I fancied getting my first of the season here. Before the game, I thought 'this is the day'.
"This is by far the highlight of my time here, easily. It was a good result and it was nice to get on the score sheet. It felt great. The lads played well and deserved it.
“I just remember Bellers [Craig Bellamy] running down the wing, Jose on the overlap and putting a great ball in. Dirk [Kuyt] let it run and I was lucky enough to finish it."
Midfielder Stewart Downing revealed the rest of the squad are delighted Carroll is finally off the mark this season, and hopes his team-mate will now go from strength to strength.
"Andy's off the mark now and we're all delighted for him," he told reporters. "Even without scoring, he's been doing really well for us.
"But getting a goal is a real bonus and for it to happen in the derby is extra special for him. He deserved it for his all-round play and it was a great finish.
"Andy is a quality striker and I'm sure he'll build on this. It was such an important goal as this was a big win for us."
But while he is happy with his first goal of the season, Carroll insists he is concentrating on maintaining his level of performance in the tough games ahead.
"We have been doing well,” he added. “Obviously there was a blip against Tottenham but the lads have been keeping together and we showed that spirit in the derby.
"Scoring against Everton and beating them at their place is special but you have to keep it going.
"We've got Man United next game and I've got to make sure I keep doing well week in and week out now.”