Such sides have long been considered minnows, and England big fish in world football, but Iceland's stunning run last summer has indicated 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 tournament exit.
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 try to do what we didn't."
He added: "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," Dier said.
"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."
Chris Smalling was forced out of the England squad through injury earlier on Friday, leading Middlesbrough defender Ben Gibson to receive his first call-up.
Southgate will also be without the suspended Gary Cahill and injured Phil Jones, giving him a headache in central defence, a position Dier is capable of stepping into if required.
Gibson is already well known by many in the England squad.
"He's a very good player getting a lot of praise for how he's playing this season," Dier added.
"I'm not the only one who knows Ben quite well, there's quite a few - Prowsey (James Ward-Prowse), Nathan Redmond, Raheem (Sterling), Stonesy (John Stones), Dele (Alli).
"A lot of people have played with him in younger age groups so it'll be quite easy for him.
"I'm sure he'll be just fine."
Dier was also asked whether England are a side who should be aiming to peak for the 2018 World Cup, or for a later tournament.
He said: "We might be quite young but I don't think we can play the age card forever.
"I'm 23 now. There's a few players around that age but we've all played a lot of games. Age isn't everything."
