The Nordic nation sent shockwaves through the football world when they advanced to the European Championship and Swede Lagerback said they would now try to stun their more fancied rivals, led by talismanic forward Cristiano Ronaldo.
"I would be happy with a draw only if our performance matched the result but if we deserved a win and got a draw, I’d be disappointed," Lagerback told a news conference on Monday.
"Our goal is to keep possession as much as we can. If we can’t, then we will look for fast breaks. There is a good chance that Portugal will have the ball a little bit more.
"They have special players with special skills and Ronaldo is one of the best in the world but it’s about playing against the whole team.
"We are looking forward to our Euro 2016 debut even if it's against one of the tournament's favourites."
Iceland's hopes of springing an upset will rest heavily on the form of their versatile mid fielders Gylfi Sigurdsson and Aron Gunnarsson, who echoed Lagerback's views.
"It's an unbelievable feeling to be here and what we have achieved is incredible, but we have to keep level heads and approach it like any other game," said captain Gunnarsson.
"I dreamt of this as a child and all the other players had in the back of their minds that one day we just might get to play on the big stage.
Sigurdsson added: ""We are very excited, we have waited for a long time for the European Championship to start. We are proud to be making history but our preparations have been largely identical to those we had in the qualifying campaign.
"I am sure the excitement within the squad will grow as the match draws closer and hopefully it will be a motivating factor to reproduce our qualifying form."
With fan violence in Marseille and Nice rocking the early stages of the 24-nation event, Lagerback promised the vociferous but amicable Icelandic contingent would arrive in droves to give the European Championship a party atmosphere.
"It is fantastic to have so many of them come from home to support us everywhere, they were phenomenal in qualifiers and I am sure they will behave perfectly," he said.
"Friends will enjoy the company of Iceland fans."
(Writing by Zoran Milosavljevic)
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