Roy Hodgson takes his England team to Euro 2016 on Monday insisting he wants them to resist any temptation to be "cynical" and there is no need to develop the streetwise edge Wayne Rooney has said the team should adopt.

Rooney's insistence that England needed to develop "that nastiness" after the World Cup was followed up by Eric Dier – whose football education came in Portugal – saying recently that Hodgson's team needed a more "intelligent edge" when it came to winning free-kicks and knowing "how to wind people up and how to agitate".

Harry Kane is on the receiving end of a head-high kick from the Portugal defender Bruno Alves in the friendly international at Wembley last Thursday.

Hodgson cited the example of Harry Kane's response to the red-card challenge from Bruno Alves in England's final warm-up game, against Portugal last Thursday, when the England striker was felled by a head-high kick but immediately got back to his feet and started chasing after the ball. Other players might have tried to influence the referee by feigning injury but Hodgson praised Kane for his behaviour and does not go along with Rooney's verdict that England's "honesty" is a potential weakness.

"Unfortunately, that's a very hard thing to teach," Hodgson said, to the question of whether Kane should have stayed down. "I think it has to be taught, if it's going to be taught, at a very early age to be part of your culture and I've said many times that I don't think it is part of our culture.

"Harry's first instinct, when he didn't get kicked severely, was to carry on and do something with the ball. Some people might say that's very laudable, others might say ‘You've got to go down, you've got to be cynical.' But I find that cynicism quite a hard thing to coach.

"The referee still made the right decision and Kane didn't need to go down on this occasion. There will be occasions – and I take the point – when there will be a [possible] penalty but the player stays on his feet and maybe then it will be a very relevant question. But again, all I can say is that it's hard for me, being English, to start trying to teach people a manner of playing which I've never subscribed to and they don't subscribe to.

"I won't be spending my coaching time teaching players to stay down and feign injury. I want to teach players how to defend better and attack better. That's what I've been trying to do with England for four years and will continue to do."

England's first match is against Russia in Marseille on Saturday and, having never won their opening game at a European Championship, the onus is on the team to hit the ground running. "What I've learned more than anything is: don't lose your first game, whatever happens," said James Milner, whose seven-year international career will take in a fourth major finals when he appears in France.

"It's great to win it and get off to a flying start but if you can't get that win, make sure you are solid and don't concede late on looking for the winner.

"Make sure you get a solid start, at least a draw, because as soon as you lose that first game in a three-game group you put yourselves under pressure straight away. That's the biggest thing. We'll go out there and try to win but if we're solid and make sure you at least get a point, that gives you a base."

The squad, who fly to France from Luton on Monday morning, are expected to visit their Stade des Bourgognes training base in Chantilly, north of Paris, for a light session later in the day as they seek to build on three successive – if not entirely convincing – pre-tournament victories.

Ryan Bertrand should be involved, having recovered from the muscular injury that ruled him out of the win over Portugal, although the Southampton full-back fears he may have lost his place in Hodgson's first-team lineup to Danny Rose.

While there is a realisation that England will need to improve from that display against Portugal to make inroads at Euro 2016, there is confidence that the squad can step up once the competition is under way. "We've had three wins out of three against different, but difficult, opposition without playing our best football," said Milner, who earned his 60th cap against Portugal. "We've got gears to go through and we want to peak at the tournament.

"We're doing some good things, we need to improve on other things and we can definitely play better and improve – but the squad's got a bit of everything. We can play a variety of formations, there are players with so many different strengths – pace, trickery, solid players and more defensive-minded players – so I think as a squad we've got so many options. The manager can pick a completely different team, which won't reduce in quality but will play a completely different style and fit into that game.

"So we've got different options and a lot of players who have had great seasons. The boys up top [Jamie Vardy and Kane] scored 50 goals between them, Dele Alli's had a great season, Wayne and Chrissy [Smalling] have just come off winning the FA Cup, so there are a lot of players on a high as well, so it's a good time for us to go into a tournament. You just want those boys riding that wave of high confidence and top form and taking it to France."