Dyche's team come into the meeting at Goodison Park second from bottom in the table, two points adrift of safety.
The Lancashire club have won only one of their last 11 league matches - although that came against reigning champions Manchester City - and Dyche is attempting to foster a feeling of confidence around his squad.
"I want the players with freedom which means being open-minded and a relaxed focus," he said.
"Whether others have it or not, I'm not worried about that. I just look at what we're doing, and the players are playing with that freedom."
Burnley's top scorer this season is Danny Ings, who has nine Premier League goals to his name - including in the 3-1 defeat in the reverse fixture back in October. Dyche says the England Under-21 international can sometimes expect too much of his own performances.
"Danny puts a lot of demand on himself," Dyche said. "That can be a weakness as well as a strength.
"You can't get inside someone, it's down to them to play with that freedom. I want players to play that way. It has to be a balance and enjoy it. I've told him he's best when he plays with a smile on his face.
"There's not pressure from me. We went down this road early season then had a good patch. It's not just about strikers - it's about creating the better quality of chances. We look at it as a team."
In contrast to their visitors, Everton have little left to play for this season other than league position and pride.
Roberto Martinez's side, after a run of one league win in 12, have shown improvement in recent weeks with 10 points from their past four outings and the Spaniard is looking to continue that sequence throughout the remainder of the campaign.
"The next six games are very important to set things in place for next season and take advantage of the good moment of form we are in," he said.
"From Burnley's point of view, it's been a terrific season. Sean has done an incredible job. He's been very strong with his message and the way he wants his team to play.
"I don't think there's fear of relegation [for Burnley] and that's the biggest difference. If you can play with no fear, that's a big advantage."
Martinez said on Thursday that Romelu Lukaku should be fit to play some part after missing the last two games with a hamstring injury, although Bryan Oviedo (hamstring), Darron Gibson (fractured metatarsal) and Tony Hibbert (knee) are out.
Burnley, meanwhile, have Steven Reid (calf) and Ross Wallace (knock) back available.
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