"I apologise to everyone. To the Nigerian people, the officials and my team mates," the 24-year-old told reporters after his first-half sending off for violent conduct.
With the Super Eagles leading 1-0 after a Kalu Uche free-kick and seemingly in control, Kaita foolishly kicked out at opponent Vassilis Torosidis in the 33rd minute and received his marching orders.
The Russian-based player looked aghast as he left the pitch with his shirt pulled over his head, almost heralding the Greek onslaught which quickly ensued.
Within 11 minutes Greece were level thanks to Dimitris Salpingidis's deflected strike - his country's first ever World Cup goal - and they grabbed a deserved first World Cup win with just under 20 minutes to go through Torosidis's poached effort.
"I accept the red card as a justified decision, I am very disappointed, I hope Argentina can help us out," Kaita glumly added after missing out on the rest of an entertaining match.
Victory for Greece puts them on three points with South Korea, who were trounced 4-1 by table-topping Argentina earlier on Thursday, while Nigeria have no points from two games.
Nigeria, one of Africa's great hopes for the competition, must now beat South Korea on June 22 in Durban and hope that Argentina can beat Greece in Polokwane the same day to have a hope of progressing.
Laid-back forward Nwankwo Kanu remained typically relaxed about his country's chances.
"If you look at the table it is not really bad, but we need a win," he told reporters.
"We cannot go for a draw, we have to go all out and make sure that we win and then it depends on what happens between Argentina and Greece."
Nigeria coach Lars Lagerback told reporters he had not seen the sending off, or spoken to Kaita about it but the Swede did reserve some praise for his side's second-half display.
"In the circumstances I am proud of the attitude and the work that they put into the second half and I hope that the Super Eagles fans back home also can see and appreciate that."
Lagerback could face some selection problems at left back after losing both Taye Taiwo and Elderson Echiejile to injuries during the defeat.
