The young Lions were leading 1-0 at the time of the sending off, but the 10 men conceded two late goals, losing the game which jeopardises their chances of reaching the semi-finals.
The 21-year-old apologised to the France bench immediately after injuring Bamba’s ankle, with the Lille winger, while not suffering a fracture, will miss the rest of the tournament with severe bruising, it was confirmed on Wednesday.
Describing the dismissal as the worst moment of his career, Leicester midfielder Choudhury said: “I just want to let everyone know that I know I have let them down. I just want to get that message out there and really apologise.
"I remember that the ball was there to be won but, honestly, watching back it looked like I was over-aggressive. It wasn’t malicious and I didn’t want to hurt him whatsoever.
“I saw the ball and tried to take it but I mistimed it. I don’t think I have ever felt worse in my footballing career than I do right now. I have let the lads down, I have let the country down. I understand playing at this level comes with a certain pressure.”
Choudhury is now suspended for Friday’s must-win match with Romania and will have to wait to discover if he will be banned for a second match.
The Foxes man has clearly been distressed by the tackle but said that his team-mates have been really supportive.
“I will go back and think about it,” he added. “The next time I get in that situation, I won’t make that tackle. Right now, I am just upset.
"The lads were brilliant with me to be honest; they picked me up off the floor, they told me to keep my head up. But right now, I can’t. I just can’t. It’s a really difficult time.”
The young midfielder’s only other red card of his career came three years ago, while on loan at Burton Albion.