To earn their first berth in the last 16 since stunning the world in their first World Cup campaign as an independent nation 16 years ago, the Croatians will in all probability need to beat Mexico in their final Group A clash in Recife on Monday.
Coach Niko Kovac said his side would have to improve on their occasionally casual defending and slack finishing against Cameroon to have any chance of progressing.
"We let (Cameroon) have too many chances and we still have much potential left," he told reporters.
"It will be important for the team to get a good rest before the Mexico game because they are an aggressive and strength-sapping team.
"But we will be buoyed by our performance against Cameroon and I must congratulate my players for an excellent performance in difficult weather."
The result left the Croatians third in Group A on three points from two games, one behind Brazil and Mexico.
Evergreen 34-year old striker Ivica Olic rolled back the years to put Croatia ahead after 11 minutes, becoming his country's oldest scorer in the World Cup when he swept home a sharp low drive by Perisic.
Cameroon, who cannot now qualify from Group A after losing their first two games, were reduced to 10 men five minutes before halftime when Alex Song was shown a straight red for needlessly hitting Mario Mandzukic.
The robust striker, helped by a mature performance from playmaker Luka Modrc who shrugged off a painful foot injury, then stole the show after Ivan Perisic seized on a poor clearance by Cameroon keeper Charles Itandje to make it 2-0.
MEMORABLE DEBUT
Back after suspension ruled him out of the tournament's opening 3-1 defeat by Brazil, Mandzukic headed the third on his World Cup debut just after an hour and tapped in his second as Croatia strolled to a comfortable victory.
A pale shadow of the side that reached the 1990 tournament's quarter-finals, Cameroon, who have won only one game in their last five World Cups, finished in disarray with defender Benoit Assou Ekotto appearing to head-butt team mate Benjamin Moukandjo.
"This hurts, a result like this. I know it's hard to play 11 versus 10 but it's not necessary to lose control like that ...," said Cameroon coach Volker Finke.
"I'm sorry about this result but we have to look forward because in this team I think there are also some players for the future.
(Writing by Zoran Milosavljevic; editing by Justin Palmer)
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