Portugal made it to the semi-final in 2012 and are desperate to go all the way this time around, with Lagerback expecting a difficult match in Saint-Etienne.
"We are looking forward to playing Portugal, even if they are a very strong team and one of the favourites to win the tournament. The squad is in fine shape and I hope we can cause Portugal some problems," Lagerback said at a news conference.
"I will be satisfied with a draw if we don't play well and still get a point, but I will obviously not be happy with a draw if we deserve more. You can't say anything about that in advance. We don't have much preparation left to do. I don't want to bore the players. It's about getting them in the right mood. They are all mentally strong, so I'm not too worried about that.
"Our goal is to try to keep the ball and play fast if possible. But I think Portugal will see a bit more of the ball. They have a lot of variation in their team, more than in the past. But I think they will dominate possession. We will try to play aggressive if we can."
Much will depend on the form of Cristiano Ronaldo if Portugal are to go far and Lagerback has stressed Iceland will obviously be keeping a close eye on the Real Madrid star.
"Of course, if a team has a special player with some special skills, we will keep an extra eye on him," he added.
"Ronaldo is one of the best players in the world. But it’s about playing against the whole team. But we will obviously do our best to close down Ronaldo."
Lagerback made headlines in the build-up to the match when he accused Ronaldo, and club-mate Pepe, of playacting and the Iceland coach once more made it clear how he feels about "unfair" behaviour on the pitch.
"I've said for many years that I dislike acting on the pitch. I think we should be able to suspend players for playacting and for trying to influence the referees," he continued.
"I am seeing it in football everywhere, not specifically at Portugal. I mentioned Pepe before because of his behaviour in the Champions League final and we all saw that. I think it is unfair and very unprofessional."