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Burnley manager Sean Dyche says his side "do not deserve to be better" than their lowly league position after being thumped by Everton at Turf Moor.
"The margins are super fine and the challenge [we face] this season is we haven't kept the margins tight," said Dyche, whose side are 18th, three points adrift of safety.
"There are a number of reasons why, but there's no excuse."
Yerry Mina, Lucas Digne and Gylfi Sigurdsson found the target as the Toffees, who went into the game on the back of two consecutive defeats, went 3-0 up after 22 minutes.
Ben Gibson got Burnley on the scoreboard before the interval but Digne added an impressive long-range second in the second half and substitute Richarlison scored a fifth late on.
The Toffees, who suffered a 6-2 mauling against Tottenham in their last outing, raced into the lead after just two minutes courtesy of Mina's towering header.
Joe Hart could only palm Digne's excellent free-kick into his own net before Ben Mee was penalised for handling the ball inside his own area.
Sigurdsson sent Hart the wrong way as Everton put their thrashing by Spurs firmly behind them, but Gibson's goal after a goalline scramble gave the hosts some hope heading into half-time.
Burnley were much brighter in the second half, but as they chased the game they left space behind for the tricky Bernard to exploit.
The Brazilian did not get on the scoresheet, but his cushioned pass to Digne set up the Frenchman to drill the ball into the far corner and put the game firmly to bed.
Richarlison came off the bench to add the fifth as Everton moved up to eighth in the Premier League.
With Sunday's heavy defeat by Spurs still fresh in the memory, Everton were determined to produce a blistering start at Turf Moor.
Boss Marco Silva left the talismanic Richarlison on the bench while Mina returned to the starting line-up after missing the defeat by Tottenham.
And the Colombia international, who cost just over £27m this summer, rewarded his manger's faith with an excellent performance.
After giving the visitors the lead in the second minute, Mina was also excellent at thwarting Burnley's fightback at the other end once Gibson's goal had given them a foothold in the game.
The 24-year-old won more duels than any other Everton player (24), as well as winning the most aerial duels for his side.
His strength and pace mean he is a powerful defensive presence, but he also had the most touches of the ball (79), indicating his ability to play out of defence.
After the disappointment of missing out on selection against Spurs, his performance at Burnley was a statement Silva will find hard to ignore.
Burnley are in big trouble, and they found themselves three goals behind before they even registered a shot at Jordan Pickford's goal.
Sean Dyche opted to start Sam Vokes for the first time since November, in anticipation of a physical battle against Everton's three towering centre-backs.
But their problems are at the other end and the hosts struggled to contain Everton's speed and guile through the middle.
Burnley have now conceded 41 goals after 19 games this season - two more than they did in the entire 2017-18 campaign.
Bernard, Sigurdsson and Walcott pulled the strings as Everton enjoyed large spells of possession, having killed the game as a contest in the first quarter.
Gibson, who was making his Premier League debut for the Clarets following his summer move from Middlesbrough, handed his side a lifeline with a scrambled goal.
And Tarkowski could have reduced the arrears to just one goal, but his side-footed effort from close range sailed over the bar.
Digne's second ended the last of Burnley's resistance after 26 minutes of the second half, and Dyche's side will need to produce more at either end to arrest their current decline.
Burnley all at sea in defence - the stats
Burnley boss Sean Dyche told BBC Match of the Day: "They started much brighter, much sharper with more energy. They were the better side and deserved to win.
"The last 10 minutes of the half we deserved to get back in it and the game settled. We got a bit more on the front foot, scored a goal and all of sudden the next goal is vital.
"The chance for Tarkowski is massive. If we put that in, after what happened to Everton against Tottenham the other day, then it may change the whole event. We then started the second half the brighter and you never know from then. But it didn't go in and the game went after that."
Everton boss Marco Silva speaking to BBC Match of the Day: "The first thing I'd like to say is this is for our fans and our players.
"The fans welcomed our players before the match, which is fantastic after a tough result on Sunday. And the players as well, they deserve this.
"It was a good win for us and now is the moment to rest and prepare for the other quick games."
On responding to Sunday's defeat by Tottenham: "I think the best solution to the last result was to play as quickly as you can, luckily for us we played after three days.
"They showed they are here to fight, to compete and to show the ambition we have as a club."
On goalscorer Lucas Digne: "I think the credit has to go to all the squad and not just one or two, but of course Lucas Digne has done well and settled. We never had any doubts about his quality or his attitude. His left foot is fantastic."
Burnley entertain West Ham at Turf Moor on Sunday, 30 December (14:15 GMT), while Everton are on the road again as they travel to Brighton and Hove Albion on Saturday, 29 December (15:00 GMT).
