"Because they haven't made it to a final tournament before, it makes it extra big for them," he told Reuters in an interview before the first leg in Reykjavik on Friday.
"From being a small country and not believing it in the beginning, it's bigger in that way," said the 65-year-old veteran who took Sweden to five major championships in a row in 11 years and coached Nigeria at the 2010 World Cup in South Africa.
"They didn't have any huge hopes after a few tough years. If we do it, it would mean a little more than qualifying with Sweden."
Lagerback showed his usual modesty, playing down his own role and saying there were many factors resulting in the tiny island nation being on the brink of qualification.
"Six or seven years ago they built seven full-size indoor pitches. That means that they can train and play football year-round," he said.
"Then there's been a generation of young players who went to the 2011 European U21 finals in Denmark. They're the framework of the team now. A lot of them have gone to good clubs and they're all playing."
In previous years even the most ardent football fan would be hard-pressed to name an Icelandic player other than former Barcelona and Chelsea striker Eidur Gudjohnsen.
But the likes of Kolbeinn Sigthorsson (Ajax) and Gylfi Sigurdsson (Tottenham Hotspur) are starting to put the country on the football map.
Lagerback said resources were less available in Iceland and he does his own video analysis of opponents, a task usually given to the coach's staff.
He splits his time between the two capital cities, working as a football pundit for cable TV station Viasat in Sweden before heading over to Iceland for weeks at a time.
Success has also led to a huge growth in interest in the team. Tickets to Friday's match sold out in two hours, contrary to many previous internationals.
Lagerback's pride in reaching the playoffs is obvious, but he is not content to stop there.
"We have been underdogs the whole time. Many asked me when I took the job, ‘why take Iceland? What chance do you have?'.
"If we succeed now, when nobody has given us a chance - you heard the playoff draw, everyone wanted us - if we do it, it would mean a little more than qualifying with Sweden."
(Editing by Tony Goodson)
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