This is the third time Greece let in an early goal at a World Cup after conceding a second minute goal against Argentina in 1994 and a seventh minute goal in 2010 against South Korea in their group opener of their two previous appearances.
This time it was the fifth minute when Colombia struck to take the lead and finish off their opponents with two more goals in the second half.
"Some of my players have to understand there are more group games coming, this is not over," Santos told reporters. "Some of them did not seem to realise where we are and what we have to do."
The Greeks, who have never progressed past the group stage and have conceded at least a goal in every previous World Cup game, are once more with their backs to the wall early in a tournament with Japan, who lost 2-1 to Ivory Coast on Saturday, awaiting on June 19 in Natal.
A second defeat will see them almost certainly eliminated from the competition.
Santos will have to act quickly if they are to have any hopes of advancing with changes to a team that played well after falling behind but squandered several good chances to score.
Left back Jose Holebas was again the Greeks' weak link - just like two years ago at the Euro 2012 - with the Colombians in the first half alone charging 62 percent of the times down his side and just 12 percent across the other side of the pitch.
Colombia's Juan Cuadrado repeatedly left Holebas rooted on the spot, including when he charged past him to float a low cross in the box for his side to take the lead.
Santos refused to single out his player for criticism but said: "We knew Cuadrado would play like that. There were mistakes made."
Another change he could be considering is introducing Yannis Fetfatzidis from the start after the highly-skilled diminutive midfielder instantly added some badly-missing spark down the right when he came on against Colombia in the second half.
Santos could also start with striker Kostas Mitroglou, only recently back from a knee injury, after 34-year-old veteran Fanis Gekas' contribution to the game on Saturday was a solitary header onto the crossbar.
Mitroglou, Greece's top striker, was brought in late in the game but had little time to make any impact but that could change against Japan next week.
"This defeat makes things very difficult for us," Santos said. "I will talk to my players, we will study our mistakes and we will correct this situation."
"We will present ourselves in a much better state in the coming two games," said the Portuguese.
(Reporting by Karolos Grohmann, Editing by Nigel Hunt)
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