The Scandinavian nation - ranked 54th by FIFA - finished second to Switzerland in Group E of qualifying and are now 180 minutes from reaching their first tournament.
Portugal, Greece, Sweden or Croatia are among the teams that they could face for a place in the South American showpiece, and Lagerback said that anything could happen.
"To qualify for the playoffs is of course a big achievement for all countries, but this is truly something special," Sky Sports News quotes the 65-year-old as saying.
"We were definitely the underdogs. When you are in the playoffs, everything can happen and with the team we have got, we can always win over two matches.
"Everything is possible, we can climb over volcanoes with these lads."
Lagerback, who led Nigeria into the 2010 World Cup in South Africa, took charge of Iceland in 2011.