The Greeks got off to a dreadful start in Belo Horizonte as Pablo Armero found the net after clever wing-play from Juan Cuadrado with just five minutes on the clock.
Greece gradually improved and ensured a more even second half, but Teofilo Gutierrez doubled Colombia's lead just before the hour mark and while Theofanis Gekas almost pulled one back when he struck the crossbar with a header, the Greeks ultimately failed to claw themselves back into the game as James Rodriguez added a third in stoppage time.
Samaras, though, is adamant that Colombia were not three goals better than Greece, noting Pekerman's team were simply more clinical.
He told FIFA.com: "We have more to give at this tournament, but I think we showed something.
"It was a strange game. For the first five or six minutes, we didn't seem to be 100 per cent in it and we conceded a bad goal.
"But after that, we had a lot of possession, a lot of pressure, and created some quite good chances.
"But, look, that's football. Colombia didn't have any more chances than we did but they scored three goals and, whether or not the result is fair, we have to face up to it.
"All we can do between now and then is keep positive, keep going and continue to play the same kind of football.
"We created chances against Colombia and that's something we can't forget. On another day, it could have been us winning, and that's something we need to take into this massive match (against Japan on Thursday)."
Despite the opening defeat, Samaras feels that Greece will have surprised many people with their positive style of play, and the former Manchester City man says their philosophy will not change.
He added: "I know what everyone expected of Greece though; that we would have 11 men behind the ball, defend, defend, defend and give everything to keep a clean sheet.
"But I think what they saw was a team that likes to attack, that moves the ball really well, and that tries always to create chances.
"We went out to win against Colombia, and that philosophy will not change. We just hope it brings a better result for us because Japan is now a must, must-win game for us."
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