But coach Lars Lagerback said the players had made it clear they were not satisfied with performances so far.
"I always believe we can win the football game and with these guys it's quite possible," he said.
"We had a team meeting yesterday and (co-coach) Heimir (Hallgrimsson) stepped in and said a few words about not being satisfied. We've only taken the first step now. But what we do on the training pitch in the next few days is most important. We're not satisfied with how we performed, especially with the attacking part. We would like to take another step against England."
Arnor Ingvi Traustason, whose injury time-winner against Austria sent Iceland through, was also upbeat about facing England.
"As a team we can beat anyone," Traustason said.
The team is staying grounded, and even the wildly joyous commentator on Icelandic TV prompted no more than casual recognition among the players.
"We're kinda used to it," Traustason said.
Despite having a dentist as joint-coach, a movie director in goal and a squad of mostly unheralded players, Bjarnason said the side was not celebrating.
"We try to focus as much as possible on ourselves and not get carried away with the people at home," Bjarnason said. "We're still hungry, we still want to get a good result against England. We're going to give 100 percent for the victory, so we can't be focused on celebrations."
Lagerback, who shares duties with dental surgery owner Hallgrimsson, has overseen a steady improvement since taking over in October 2011, steering Iceland to a 2014 World Cup playoff against Croatia, and then securing qualification for its first European Championship.
Lagerback can draw on plenty of experience from leading his native Sweden to five successive tournaments and the 67-year-old paid tribute to the influence of two Englishmen - Bob Houghton and current England coach Roy Hodgson - upon him and Swedish football.
"Roy has definitely been both, from my point of view anyway, a good friend and an inspiration for my coaching career," said Lagerback, who said the English influence had spread to Iceland, too.
Despite the friendship, Hodgson can expect no favors from Lagerback, whose players would like nothing more than to beat their heroes. English football is immensely popular in Iceland, where supporters often cheer the England team during tournaments.
Bjarnason used to be a Manchester United fan when he was younger. He joked about exchanging jerseys with Wayne Rooney on Monday in Nice.
"If he asks me, I'll give him my shirt, yes," Bjarnason laughed. "He's a great player and he has been for England over the years. He has a lot of experience. He probably hasn't played his best game yet at the tournament and hopefully he won't do that against us either."