Pablo Armero, Teofilo Gutierrez and James Rodriguez were on target to ensure Greece's World Cup campaign got off to a miserable start in Belo Horizonte.
The Euro 2004 champions were not completely bereft of chances, with Theofanis Gekas hitting the crossbar from six yards out for a chance to pull a goal back when the South Americans were 2-0 up.
The defeat dents Greece's hopes of making it out of a World Cup group for the first time, but Santos insists all is not lost.
"It's not a tragedy," he told reporters. "It is a setback that complicates the situation.
"I will talk with my players, we will look at our mistakes to correct the situation and in the next two matches we will present ourselves better.
"Congratulations to Colombia, they were the better team and fairly won 3-0. We had opportunities, we had effort but we paid for our mistakes."
Greece will hope to turn their World Cup fortunes around when they face Japan on Wednesday before clashing with Cote d'Ivoire on June 24. The European nation's upcoming opponents face each other at 03:00CET on Sunday.