The South Americans were rocked when talismanic striker Radamel Falcao lost his battle to be fit for the finals after suffering a serious knee injury playing for French club Monaco in January.
Immediately, Jose Pekerman's team lost a man who has scored 20 goals in 51 internationals since his debut in 2007.
The 28-year-old was his country's top scorer in the qualifying campaign as his nine goals helped Colombia make the finals for the first time since 1998.
In the absence of Falcao, Teofilo Gutierrez, who plays his club football at River Plate in Argentina, is expected to carry his team's goal-scoring burden starting against the Greeks.
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Colombia, whose best World Cup run was a last-16 appearance in 1990, have 18 players who feature in the European leagues.
One of those is Falcao's Monaco teammate James Rodriguez, a key figure in midfield who is a genuine threat from free-kicks.
However, his appetite for the hard yards of defence has often been called into question.
Martinez believes the 2014 Colombia team has more talent than the 1994 squad who went to the United States finals as one of the favourites but flopped in the first round.
"Ivory Coast have very experienced players with a lot of quality, Japan are always at the World Cup and cover every blade of grass, and Greece are tactically very strong.
"When you're at a World Cup, the first thing you say to yourself should be, 'We don't know how far we're going to go, but we do know how far we want to go'.