With eight spots up for grabs from nine play-off groups, the Scandinavians were the unfortunate nation to miss out by virtue of picking up fewer points then the other European runners up.
Italy ended Armenia's hopes of progressing to next year's World Cup with a 2-2 draw in their final qualifier in Naples.
Italy booked their ticket to the finals in Brazil by topping the group while Armenia finished second from bottom after starting the day with an outside chance of claiming second spot and a place in next month's play-offs.
Bulgaria's disappointing campaign ended on a sour note with Borek Dockal's second-half goal securing the Czech Republic a 1-0 victory as the hosts finished with 10 men.
The Bulgarians found themselves 1-0 down in the 52nd minute when Dockal hit the target with a 20-yard shot as keeper Vladislav Stoyanov should have done better.
Defender Petar Zanev was sent off for a second yellow card 15 minutes from time, Bulgaria's fifth dismissal of the qualifying campaign.