Despite creating 19 chances against Fulham, the Toffees slipped to an opening game defeat at home – where the top-flight’s lowest scorers lost a record 10 league matches last season.
Central to the issue is the continuing unavailability of injury-plagued Dominic Calvert-Lewin, whose lack of minutes in pre-season means he is still possibly a couple of weeks short of being ready.
However, the arrivals of on-loan Arnaut Danjuma – who made his debut as a late substitute – and young Sporting striker Youssef Chermiti, watching from the stands, will hopefully help to ease the burden as current deputy Neal Maupay wasted a host of chances as he extended his woeful record to one goal in 30 appearances for the club.
“Dominic will get some football this week, amongst others,” said Dyche, who is still looking for reinforcements but knows he must get more out of the limited resources he has.
“He is at the end of his rehab period, so, in the next week or two, we’re going to be stronger, just by our own group and let’s see if we can get something in to help us as well.
“Arnie (Danjuma) is getting fit, properly fit – he knows he’s a bit behind the curve.
“I am confident we have to rely (on players) within the squad because this is what we are at the moment. If we can affect it, we will do.”
Everton had only 41 percent possession but made the most of it and with better finishing could have had the game won by half-time.
While the outcome was disappointing, the manner of the performance was more encouraging than the majority of the relegation scraps they had when Dyche took over in January and guided them to safety on the final day.
“Some of the breakaways, some of the moments, some of the quality of chances were excellent,” the Toffees boss added.
“One of our analysts said about xG, which I’m not that big a believer in but it’s still a reference point, was around three, which is high in the Premier League.
“Inevitably, it’s only a measure but we’ve got to look at where we were and where we are now – and that, I thought, was a big shift.
“Now we’ve got to find those moments to go and score goals.
“But there’s a real strong sign there today, a strong sign of a good outfit there that is creating lots of chances and a lot of good things, so we’ve got to maintain the belief in that.”
Fulham were fortunate to leave Goodison Park with a third successive win and boss Marco Silva admits there is plenty of improvements to be made.
“We need more time to work, our pre-season was not at the level that it should be so we missed a bit of energy,” he said.
“But we were able to win a football match and that shows we have the quality to work.”