Burnley manager Sean Dyche believes his struggling team are being punished for not pressuring referees as they attempt to stay in the Premier League.

Saturday's 1-0 defeat at Everton, courtesy of a first-half goal from Belgium international Kevin Mirallas, left Burnley bottom of the table with games running out in their survival bid.

It was a controversial reverse, with Burnley midfielder Ashley Barnes sent off for a second bookable offence just before half-time, and Mirallas fortunate to escape a similar fate following a studs-up challenge on George Boyd after the restart.

Everton were also awarded an early penalty, with Ross Barkley's spot-kick saved by Tom Heaton, even though replays clearly showed David Jones's foul on Aaron Lennon was well outside the area.

Dyche also correctly pointed out that his team might have been awarded a first-half penalty of their own at Goodison Park after Scott Arfield stayed upright despite being tripped just inside the Everton area.

"Ashley gives everything for the team and has nothing to apologise for but it was just two silly challenges, nothing malicious," said Dyche. "At least the ref got that one right, so that was good.

"I was interested in the view he had of their penalty because it was well outside the area and then Scott Arfield was dancing around the edge of their box and was tripped. If he had gone down, it would have been a penalty, but he stayed on his feet."

However, Dyche added: "But the biggest one was the Mirallas challenge. It's impossible that he could stay on the pitch after that -- I've no clue how he did.

"I have to say I don't think he is that kind of player, it's nothing about him as a person.

"But, factually, in my opinion it was a red card challenge -- it was high, late, I don't understand how he doesn't get sent off.

"We attempt not to simulate, we attempt not to surround the referee -- and other teams would for the Mirallas challenge without doubt -- yet we don't get decisions. If we surrounded the ref, maybe we would.

"What do we have to do? We do it right and get nothing; do it wrong, you get something."

Burnley host Leicester, who climbed off the bottom with a 2-0 win at home to Swansea, next weekend in a match that will have a major bearing on which of the teams retain their Premier League status.

Despite this latest setback, Dyche was adamant his players had not abandoned hope of staying up.

"Absolutely, there has never been a lack of belief," he said. "There has never been a lack of organisation, a lack of energy.

"We have been written off since one minute after we won promotion last year, so that doesn't break them. They will be ready to go again."

Everton's victory maintained their impressive recent form, although the win did raise questions regarding manager Roberto Martinez's penalty-taking policy.

Despite having Leighton Baines, the fifth-most efficient penalty-taker in Premier League history with 14 goals from 15 attempts, Martinez has handed spot-kick duties to Romelu Lukaku, who was on the bench when Everton won their 10th minute award against Burnley.

Lukaku won the position when the issue reared its head in January after Mirallas snatched the ball and missed from the spot in a goalless draw with West Brom.

"If Romelu had been on the pitch, he would have taken it, Romelu Lukaku is our penalty-taker," said Martinez.

"But we've got Leighton Baines who's a specialist, Gareth Barry who has an incredible record and people who can control big moments, like Ross Barkley.

"Ross showed incredible responsibility and Leighton Baines was happy for him to take that responsibility but, after he missed, I was pleased with the way he responded," the Spaniard added.