Dyche was without several key figures during last week's 3-0 opening-day defeat by Brighton at Goodison Park and the Toffees are still in a sticky situation regarding the fitness of their senior squad.
"We're stretched unfortunately," Dyche said Thursday. "We're down to about 14 recognised first-team players at the minute, so that's not perfect, but the challenge is right in front of us as always.
"We've lost a few bodies in pre-season, which has been unfortunate, they're searching for true fitness and we've got to get them fit and we've lost more who might not be available for this weekend."
Dyche revealed stand-in Everton captain James Tarkowski is the latest injury concern, while fellow defender Ashley Young is suspended after his red card against Brighton.
"Jarrad Branthwaite is still a bit away," Dyche said. "He is not close at the moment. A few of the lads like Seamus Coleman and James Garner are getting a bit closer and have just come back into training with the group."
The former Burnley boss added: "James Tarkowski has got a 'maybe' situation, so we will have to look at that going into the next game. We obviously know the right-back situation with Ashley Young now suspended as well."
Young's fellow right-back Nathan Patterson is still recovering from a hamstring surgery in April while striker Youssef Chermiti has been sidelined after a minor foot operation earlier this month.
"It is an ongoing challenge," said Dyche. "We haven't got much financially to correct it so we are just going to work with the players and hope they can get back to being fit and then stay fit."
Dyche, meanwhile, had no details to reveal regarding takeover speculation linking Crystal Palace joint owner John Textor with Everton, but said it was "unlikely" there will be further transfer activity at Goodison before the summer window closes at the end of the month.
"The club seems pretty steadfast with the work that we've done," Dyche said. "But with the shifting sands of football, who knows what will happen?
"But generally it's a place where everyone says 'we are where we are' sort of thing."
