Lars Lagerback has just been asked about the mentality of the Iceland players he has taken to the brink of a first World Cup finals. He pauses for a moment and then says: "There is no moaning whatsoever. No complaining. Take our travelling, for example. We are not the richest Football Association so our travelling is sometimes a little bit awkward. One time we had to wait six hours for a plane in London and no one said a word." And where were they going? "We were on our way to Cyprus."

Lagerback is an understated character. He does not have a high profile and neither does he seek one. Yet he must arguably be the best international coach in Europe over the past 15 years. He took Sweden to a remarkable five consecutive major tournaments in his capacity as joint head coach and then head coach and when with Nigeria was only an astonishing Yakubu Ayegbeni miss (from two yards) from reaching the second round of the 2010 World Cup.

Now, however, he has surpassed himself. When he took over as Iceland coach in October 2010 they were ranked lower than Liechtenstein. This week they take on Croatia in a two-leg play-off with the winner reaching the World Cup finals. If Lagerback masterminds another astonishing success, the country would be the smallest (population-wise) ever to compete at the finals.

So what did the Iceland FA say to him when he took on the job? Did it have the aim of reaching the play-offs? "They didn't have any set targets when they appointed me actually, so there was never any talk of me having to reach the play-offs or any other result," he says. "But I would never have taken the job if I didn't think we could do that. The reason I took the job was because I thought there was a very interesting group of players to work with, especially the group of Under-21 players that reached the finals in 2011 [and] a realistic chance of getting this far."

Lagerback and his team reached the play-offs by finishing second in Group E, which admittedly was not the strongest, comprising Switzerland, Slovenia, Norway, Albania and Cyprus, but he now feels they have nothing to lose against Croatia.

"Of course it would be a huge disappointment if we didn't get to Brazil now that we are so close but, as far as I am concerned, we are in a win-win situation," he says. "There weren't many outside Iceland and, to be fair, on Iceland who expected us to get this far, even though the expectations have grown the further we have got in qualifying. But I hope people are not thinking that [it would be a huge disappointment to miss out]. I am certainly not thinking that way."

Lagerback says that he learned a lot from his stint as Nigeria coach, the experience making him broadening his horizons. It may not seem as the most obvious career move (Nigeria to Iceland) but the 65-year-old Swede says he did learn a lot by taking the African country to the World Cup finals. "The biggest differences were off the pitch, not on it," he says. "If you come from abroad to a new country you have to learn as much as possible about that country, its culture etc before you start. When I worked with Nigeria I got a lot of help from my team secretary whom I just squeezed every drop of information out of for a couple of weeks. I try to adapt very much to the culture of the team I am coaching.

"Football-wise there are very few differences actually. They [the Nigerian players] were very professional on the pitch but very different off the pitch. And leadership-wise I had to act a little bit different as well. They were vey sensitive to criticism and it wasn't right to criticise anyone in front of the group."

There is no secret to his coaching philosophy, he says, but there are a few key ingredients he feels are crucial to create a successful team. "I've been involved in international top football since the early 90s, travelling around with [Sweden manager] Tommy Svensson and scouting opponents while working with the youth teams before I started with the men's senior team, and I would say the thing that stands out for every successful team, notwithstanding good players, is to have a very clear idea of how to play, a clear plan. You have to get the team to work together in a good way, that is also absolutely crucial. If you look at all the good teams, from Spain to Barcelona and other teams who have won tournaments, whether it is international or club football, there is always a very clear idea of how to play football. And if you can't adhere to that, then it is very difficult to achieve anything."

The fact that he does not speak Icelandic has not been a problem, according to Lagerback: "We do speak a lot of English. There are quite a few players who understand a "Nordic" language [and therefore Swedish]. Individuall I can speak Swedish to the players but when we are in a group I always speak English.

"I think I get pretty much everything through to them [despite English not being my first language]. It is possible that some of them will lose a detail or a nuance of the team talk but I don't actually think so. For, tactical theory is an important complement to what I do but the most important part of what you do is out on the pitch. But all in all I think they get pretty much everthing. A lot of these players have a very good grasp of English, like people do in Sweden. A lot of them have lived abroad for long periods of their lives and a lot of them have played in England as academy players even though they are not playing there at the moment."

Two players with an English connection have been instrumental in Iceland's successful campaign. Eidur Gudjohnsen, the 35-year-old who spent two years at Bolton and six at Chelsea and now plays for Club Brugge, and Tottenham Hotspur's Gylfi Sigurdsson.

Lagerback says that Gudjohnsen has a wonderful "football eye" and it is easy to understand what he means. "He wasn't with us in the first year as he had a serious injury but then he came back in the autumn," Lagerback says. "And since then he has been very professional and a very positive person in the group and he has an extremely good 'football eye'.

"Gylfi, meanwhile, can definitely go very far. He has been outstanding this autumn. He has been good throughout the qualifying tournament but taken another step up. He is a unique player for me when he gets a central role, and he doesn't have that at Tottenham, but he is a fantastically good football player. He is an extreme team player and can work very, very hard for the entire 90 minutes so for Iceland he is worth his weight in gold."

And that, one presumes, is what the manager's employers think of Lagerback. Iceland start at home against Croatia on Friday and it feels as if the Swede may already have the upper hand on his counterpart, Niko Kovac, who has just replaced Igor Stimac as head coach for the visitors.

Recently Lagerback was talking at a coaching seminarium the 42-year-old Croat attended and taught him a few things. Not everything, though, and when teacher meets pupil in the two-legged play-offs it would be foolish to bet against the former.

Lagerback said: "It is very difficult to know how the change of coach is going to affect our games against them. But we have a lot experience of playing teams with new coaches in place. This is the fourth team we will play in this qualifying campaign have have just appointed a new coach. Slovenia, Cyprus and Norway all had new coaches when we faced them.

"What I have understood and hear – I mean they have lost three and drawn one game of their last four so … – so the atmosphere probably wasn't the best in the squad.

"We have, of course, been through their matches and you could clearly see that it was not a team in harmony, when they played Scotland for example. I think mentally it will probably be a fillip for Croatia to have a new coach.

I know Kovac a little bit but football-wise I don't think it is an advantage to change coach when you've only got four or five training sessions to prepare for a game. He can't do that much in that short period of time."