Nigeria took an early lead in Bloemfontein through Kalu Uche but the match turned on a red card for midfielder Sani Kaita just after the half hour, dismissed after kicking out at Vasileios Torosidis.
A goal just before half-time for Dimitrios Salpingidis and a second half winner for Torosidis won the game for the Euro 2004 champions, who registered their first ever win at a World Cup finals at their fifth attempt.
A frustrated Lagerbäck, who said the sending-off changed the course of the game, said he could not see the incident clearly but described it as “very, very, very strange” and called for more dialogue with referees.
“Everyone who knows anything about football knows that if you are playing with 10 men at this level it’s much more difficult to win a game,” he added.
The Swedish coach said he was pleased with the way the match unfolded from the kick-off.
“We started the match quite well and I think we controlled the game. We got the goal, then you have the sending-off and we had some problems,” said Lagerbäck.
“With the circumstances, I’m proud of the attitude and the work that the players put into the second half,” he added.
He said the coaching staff would take stock of the defeat before gearing up for Tuesday’s match against South Korea, where a win could still see the Super Eagles qualify, with Greece up against table-topping Argentina on the same day.
Lagerback said: “The positive thing is that we still have a chance of qualifying, although we need a helping hand from Argentina. We need a fresh start, and we’ll do that by beating Korea Republic.”
But captain Joseph Yobo was downbeat about Nigeria’s chances of qualifying.
“Until the sending-off we had the game under control. After going a man down our aim was to try and dig in for the draw.
“Our attitude was good in the second half and we showed character, but it’ll be very hard now.
“We’ve lost both matches and it looks like we won’t make it to the next round, even if we win our last game. We’re basically out of the tournament.”
Nigeria’s defeat continues a miserable run for the Super Eagles in which they have gone seven games without a win at World Cup finals – including six defeats – since their last victory in France 1998.
Argentina, Nigeria’s conquerors in their first match, beat South Korea 4-1 in Johannesburg in the earlier Group B match to take their tally to six points. South Korea are on three points along with Greece, with Nigeria yet to register.