The 22-year-old, whose form and fitness has come into question in recent weeks, opened the scoring at Goodison Park with 20 minutes remaining.
"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."
The £35m signing from Newcastle United has now scored four competitive goals for the Reds.