Such sides have long been considered minnows, and England big fish in world football.
But Iceland’s stunning run last summer has clearly indicated that the gap is closing.
Midfielder Dier played the first half of England’s defeat in Nice last June, as Roy Hodgson’s side made a humiliating exit from the tournament.
And partly because of that experience, Dier insists England will be ready for anything Lithuania have to offer in this weekend’s World Cup qualifier at Wembley.
Looking back to the Iceland experience, Dier said: “Whenever you’re in an England squad you’re going to think about it.
“It’s a painful reminder and it’s a good lesson for the future.
“We can look back on that game and what we didn’t do, and in games like the one on Sunday
“It’s going to be a tough game. In all internationals now there’s no really easy games.
“Every team sets up to try to stop us, especially here at Wembley.
“We have to be confident going into it, try to play quick, attacking football and hopefully they won’t be able to handle that.
“It’s key we play with intensity, move the ball quickly.
“I think we need to be aggressive with the ball, move it quickly, and hopefully create a lot of chances and make it exciting for the fans.”
The Group F game is England’s first qualifier since Gareth Southgate became the team’s permanent manager, and will follow four days on from the 1-0 friendly defeat to Germany in Dortmund.
Dier played in that game and has become an England regular in a short space of time.
The 23-year-old Tottenham midfielder even fancies the England captaincy one day.
“It’s an ambition of mine. I’d love to one day be able to do that,” said Dier.
“That’s something the manager decides and I’m sure he’ll pick who he thinks is best.
“I think I’ve always had qualities that a captain may have and I think I can do that job.”
Dier, meanwhile, has called on England fans to support the Three Lions “in the right way” – especially in the wake of the appalling Westminster terrorist attack.
England’s friendly defeat to Germany was marred by fans booing the German national anthem and singing distasteful songs leading FA chairman Greg Clarke described the chanting in as “inappropriate, disrespectful and disappointing.”
The incidents came on the same day a terror attack in London which left five people dead, including the attacker and a police officer.
The FA is planning a number of tributes to the casualties, with black armbands, a minute’s silence, a reef-laying ceremony and the Wembley arch being coloured red and white throughout the game – which will also be attended by a number of distinguished guests.
And Dier, set to pick up his 17th cap in the game, wants supporters to show they can be portrayed in a positive light after such a turbulent week.
“In general, the fans have been fantastic with us wherever we go,” he said.
“The support they give us is always amazing.
“But all we ask is that they support us in the right way and they’re respectful.
“Because of the dreadful things that happened in London we just hope the fans are very respectful of that and us as players we’re going to respect everything in the right way. We’re going to do everything to honour the people who passed away this week.”