Manchester United took the lead with a penalty goal by Cristiano Ronaldo but Liverpool hit back four times to make it 4-1.
Gerrard told Sky Sports: “The important thing is that we have made the gap smaller (United lead by four points, but still with a game in hand).
“We realise that Manchester United are a fantastic team and there’s still a lot of work to do.
“We’ll need a little bit of luck along the way but hopefully that gives teams that are going to play against Manchester United a bit of belief that they can be beaten.
“And hopefully it will give us a lot of confidence to go on and win as many games as we can.”
He added: “I’ve been lucky enough to experience winning here before and that was also a magnificent feeling, but to score a goal after all the stick I’ve had from United fans over the last 10 years – well, it’s nice to score and rub it in a bit.
“It was magnificent, a great team performance. From front to back we worked very hard today, showed great character after going a goal down and it was a magnificent win.
“In the end it was comfortable with a man being sent off, but I think we were men today, we controlled the game. It’s not very often you see Manchester United getting beat 4-1 at home.”