Having given Croatia a 27th-minute lead in the second leg of their playoff after the sides had played out a goalless draw in Rejkyavik, Mandzukic was dismissed 10 minutes later for a studs-up lunge into Johann Gudmundsson's groin.
Croatia shrugged off the striker's dismissal, however, and took the contest to Iceland in the second half with captain Darijo Srna sealing victory just two minutes after the break.
Mandzukic regretted the rash challenge but admitted the joy of scoring outweighed the disappointment of any ban he will need to absorb in the group stages of next year's finals in Brazil.
"The important thing is that we are through and I am really not thinking whether I will miss any of the games... or how many," the Bayern Munich forward told reporters.
"I scored one of the most important goals of my life but I trembled after being sent off as I was completely unnerved about the prospect of turning into a villain if Iceland equalised," he said.
The Croatians ended a five-game winless streak with a solid performance after a tepid stalemate in Iceland which came on the back of poor end to their qualifying campaign in Europe's Group A.
DIFFICULT DAYS
Following a 2-0 loss to Scotland in their final group match, Niko Kovac took over as coach from the sacked Igor Stimac and was able to steer the country to an eighth major tournament out of 10 attempts as an independent nation.
"Our team morale came to the fore after Mandzukic was sent off and I think everyone played within their limits, excelling both defensively and coming forward," Kovac said.
"It's been the 10 most difficult days of my life because I am a young and inexperienced coach.
"I want Croatia to be mobile in defence and creative in attack, this is my concept of football and now that we have qualified for the World Cup, we must start nurturing this style at grass-root level," the 42-year-old added.
Kovac, who scored 14 goals in 83 appearances in Croatia's midfield, thanked his predecessor for taking the side to within reach of the finals.
"Stimac clinched a runner-up spot in a very tough group and he deserves plaudits for putting us in the position to qualify," he said. "Now it's up to us to prepare for the World Cup and be in the best possible shape in Brazil."
(Editing by John O'Brien)
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