Everton manager Ronald Koeman is not one to get carried away so it was unsurprising that he reacted to their best ever start to a Premier League season by focusing on where they needed to improve.

Everton made light work of promoted Middlesbrough on Saturday, fighting back from going behind to win 3-1, with midfielder Gareth Barry marking his 600th Premier League appearance with a goal.

Further efforts from Seamus Coleman and Romelu Lukaku wrapped up a victory that lifted unbeaten Everton back into second in the table after five games.

They are two points off leaders Manchester City, but Koeman, who arrived from Southampton in the close season, is demanding more from his players.

"They need to run more and they need to press more and then you make it difficult for your opponent," he told the BBC.

The Dutchman has led a swift turnaround in Everton's fortunes after they finished last season in dismal fashion, winning once in 10 league games before former manager Roberto Martinez was sacked.

Koeman has now won four straight league games following their draw with Tottenham Hotspur on the opening weekend.

"First it's a good start in results and in points, but the most important thing is the way we got the points," Koeman said.

"You see the reaction of the fans, they like it how we play.

"The team is more aggressive than it was, that's what we like to be in football."