The Manchester City attacker has been ruled out for two months following a tough challenge by his France team-mate, with the centre-back relieved he will not miss the World Cup
The centre-back strongly challenged his France team-mate in the second half of his side's 2-0 Premier League defeat, with City boss Manuel Pellegrini claiming he should have been shown a straight red card.
It was initially feared the 26-year-old may be out for several months with a medial ligament injury in his knee, but it has since been confirmed that Nasri will be sidelined for around eight weeks.
"I was waiting to meet him in front of the changing-room door but he got treatment," Yanga-Mbiwa told L'Equipe.
"Then, I immediately tried to get his phone number. I called him several times but he never answered.
"I left a message, I tried again on Monday but I failed to talk to him. I will try again because I want to apologise personally. I was so sorry.
"I just wanted to prevent him from going ahead, make him fall. He stayed upright on the first tackle, but fell on the second one.
"But I clearly didn't want to hurt him or be violent with such a gesture. I wanted to trip him up, there was no nastiness."
And Yanga-Mbiwa admitted his relief that the injury would not rule Nasri out of the World Cup.
"I finally heard it should be a two-month absence and I was relieved," he added. "When I heard it could be broken knee ligaments and it could imperil his World Cup, I felt really bad."