The Blues won 3-1 thanks to goals from Abdoulaye Doucoure, James Tarkowski and Dominic Calvert-Lewin.
“It's good to get a result our performance warranted," Dyche told evertontv. “We've stepped away twice [this season] - once against a very good Arsenal side in the second half, and at Villa we weren't close - but the other games I think we performed well.
“It's hard because you have to keep telling that story. I think the Evertonians realised [we have played well in most games] but you've got to win, you've got to score goals so to do that today at a tough place and be so effective in our play - we had 18 efforts at goal - was very pleasing.
“The biggest reinforcement is for the players. They've been working hard, they've been diligent this week, we had a chat about how we can find freedom when the noise is tough.
“At the end of the day, we have to change the story and it's a start today because the majority of our performances have been good. This is a step forward because we did win, we created lots of chances and we kept with the right on-pitch behaviours to keep pushing forward and playing.
“There were a lot of good performances and a lot of good habits but you only get them reinforced when you win games - and we've got to keep winning and keep that winning mentality and creating a different story for Everton Football Club and get our fans to believe in what we are doing.
“This is a step forward but there is a lot of work to do."