Everton thought they had the lead in the first half when defender Michael Keane had the ball in the back of the net. But referee Stuart Attwell disallowed the goal for what he perceived was a foul by defender James Tarkowski on Fulham goalkeeper Bernd Leno.
There appeared little in the incident with Tarkowski standing still and Leno dropping the ball into the path of Keane.
"I think VAR (Video Assistant Referee) is there to make sure that doesn’t go the wrong way because our defender has done nothing," a frustrated Dyche told BBC Sport.
"Tarky (Tarkowski) just stands there, the keeper catches it and drops it on his head.
"He did not try to impede him, it bounces out of his (Leno's) hands, we score and bizarrely they get a foul. That is the modern game - you touch a keeper and it is a foul."
But Dyche said Everton were also far too wasteful in front of goal and that was perhaps their ultimate undoing.
"We created four or five golden chances in the first half and were very good on the break as well. I thought we were the better side overall, but sometimes you don’t get what you deserve," he said.
"We did not finish them off, and we know from last season we have to improve at that, but we were getting the team in the right manner and the right areas.
"I was pleased with that because that is the highest chance count and quality of chance count that I can remember for a long time here."
There were audible groans from a nervous Goodison Park crowd, who watched their side survive relegation on the final day of last season, as the missed chances began to mount.
"The crowd need to stay with us because we have roughly the same group of players, we have adapted to what we are and that is what we showed today," Dyche said.