Dyche's side stormed to their first victory over their Merseyside rivals at Goodison Park in 14 years on Wednesday.
Goals from Jarrad Branthwaite and Dominic Calvert-Lewin gave Everton just their second win in the last 30 meetings with Liverpool, whose title ambitions were severely damaged by the defeat.
After being hit with two separate deductions totalling eight points for breaches of the Premier League's profitability and sustainability rules, Everton were in danger of losing their top-tier status for the first time since 1954.
But the Toffees are now eight points clear of third-bottom Luton with four matches remaining.
However, with a third successive relegation scrap almost survived, Dyche made it clear Everton's bid to return to prominence is nowhere near a successful conclusion.
"There is miles to go. It's a thing I've thought about, the truth line of the club," he said.
"There has to be a level where everyone across the board gets it. All the fans and all people at the club and I still think we are not quite there.
"We are getting towards it, some of the reality of the club: the finances and where it is and there is no quick fix. It has to be built on."
Everton host Brentford on Saturday looking for a fourth successive home win and Dyche is keen for the players to refocus quickly after the Merseyside derby.
"We've taken big steps but there is more to come. We can control the situation ourselves and that's what we've always been aiming to do even with the points deduction and we are beginning to show that again," he said.
