The Three Lions progressed to their first World Cup semi-final since 1990 with an impressive performance against the Swedes, with two headed goals from Harry Maguire and Dele Alli helping England cruise into the last four.
"England are absolutely good enough to win the World Cup", he said. "I hope that, when they look at us, they know that everything is possible and that they can also go far", Dier said.
"We had to withstand a lot of physical pressure", said England coach Gareth Southgate.
"We have seen the reactions back home and it's been unbelievable, so we will hopefully give them many more great moments".
England captain Harry Kane failed to score for the first time in seven matches for his country, but the Tottenham striker is still the leading scorer at this World Cup on six goals.
"We are aware of a small group of fans celebrating the match result in one of our stores", the statement said. "We have an outstanding mentality in these players, a humility and recognition of where they were 18 months ago and the work needed to get to here". It was England's eighth set-piece goal of its 11 in Russian Federation, and the centre back's first in worldwide football. After England's entry into the semis, Beckham posted on Instagram his own version of "it's coming home".
Alexander Zverev crashes OUT of Wimbledon in shock defeat to Ernests Gulbis
The world No 44 from France will next meet another big server in Kevin Anderson , who overcame Philipp Kohlschreiber 6-3 7-5 7-5. It was Zverev's second five-set match in a row and he came down with an illness on Friday.
Swedish great Ibrahimovic who now plays in the U.S., challenged the former England captain on Saturday to a wager on the outcome of today's game.
Although Sweden started brightly, England quickly got back on the front foot, and eventually grabbed a second goal through Dele Alli. We've just got to keep doing what we are doing. I think if you say it's an easy game in a quarter-final of a World Cup then you are pretty stupid to say that.
The Americans seem to be going off the boil with their World Cup fever, with England and Croatia demoted to the sidebar.
"We're like family really", he told a media conference on Friday.
Fabian Delph 6 - On for Alli late in the game, Delph made sure England continue to tick over in possession and resisted any comeback from Sweden.