Everton captain Phil Jagielka admits the players are scared of new manager Ronald Koeman but his strict approach is bringing the best out of them.

The Toffees had undoubtedly gone soft under previous boss Roberto Martinez and there were accusations in the final few months of his reign he had lost the dressing room completely.

His replacement arrived with a big reputation both as a player and a manager and immediately laid down the law, introducing a tougher line on standards at the training ground and taking a harder line with players, but it is already paying off on the pitch.

Everton have had their best start to a season since 1978 and are second in the Premier League after four wins and a draw.

"Yes there is a fear, definitely, just down to the fact that there have been people who have had good preseasons and they haven't started a game yet," said Jagielka.

"He is not scared of making changes. James [McCarthy] was really unlucky at West Brom, playing out of position and he got brought off before half-time because we needed to do something different tactically.

"He is not afraid of making decisions before and after the game.

"It is like being back at school with a new headteacher who is trying to be a little bit stricter.

"You only have to look at the jobs he has done. That proves he has not done a bad job.

Everton are off to their best start since 1978. Lynne Cameron/Getty Images

"At the moment it is going well. I wouldn't say we are playing amazing, but we are getting fantastic results and that breeds confidence."

Koeman's handling of Ross Barkley is a case in point. The England midfielder was hauled off at half-time in Monday's win at Sunderland and in the following days the manager told the 22-year-old he had to improve.

Barkley responded with a better performance in Saturday's 3-1 win over Middlesbrough and Jagielka believes that says as much about the player as it does his manager.

"Ross took what happened on board and it was great for the manager to give him another opportunity to perform," added the centre-back.

"It may not have been Ross' most dazzling of games but he got around the pitch, put tackles in and that is what we want from him.

"He is not going to go and crawl into a hole or hide. He has had such a lot of expectation from a young age but he has learnt to deal with it."

Koeman insisted he was not testing Barkley but he had one simple message for the player and the rest of his squad.

"If you don't handle the pressure you can't play in the Premier League," Koeman said.

One man who has coped brilliantly well so far is summer signing Idrissa Gana Gueye, who is already looking a steal at £7.1 million from relegated Aston Villa.

"He was outstanding, perfect in every aspect of football," Koeman praised.

"Of course he is winning a lot of second balls and tackles but he showed composure on the ball, always trying to play forwards.

"It is a fantastic signing for the club and I hope we keep him for a long time."

Alongside him was the evergreen Gareth Barry, who will be 36 in February, making his 600th Premier League appearance with Koeman hinting the midfielder could go on for another two years.

"It is important to have a balance in your squad, young players, experienced players, and Gareth football-wise is one of the most clever players on the pitch," said the Dutchman.

"If you don't need to run a lot of distance then he can play two years more than this season.

"We need to support him. We can't do all the training sessions which the rest do but we keep the boy fit as he is important for the team."