The Reds supporters were in full voice as they saw their team hold the defending English champions to a 2-2 draw in the Premier League.
"I think the atmosphere will be important in the coming games," Shelvey told Liverpool's official website. "When we scored against City, you couldn't even speak to the person next to you because the atmosphere was so good and the noise was so loud.
"It's good to have that behind you and ever since I have been here, the fans have been like they were on Sunday. That's why it is a great club to play for - the fans are electric.
"I think it's really starting to come together on the pitch and I think the fans saw that again against City. But you've just got to take it step by step in this league and game by game."
Liverpool will welcome Hearts at Anfield in the second leg of their Europa League playoff tie on Thursday.
The Reds lead 1-0 from the first leg played last week.