Coquelin was dismissed after collecting a second booking for a challenge on Harry Kane with his side leading 1-0 after 55 minutes.
Seven minutes later Arsenal were 2-1 down after goals from Toby Alderweireld and Kane, but Alexis Sanchez hit back late on to keep Arsene Wenger's team within three points of their north London rivals.
"I didn’t really see the goal [because I was in the dressing room] but someone came and told me that we scored the second one - it was a relief for me," Coquelin told Arsenal Player.
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"I did not want us to lose today because at 1-0 I thought we were doing great. A point today is a good point, it is a great result for us.
"I think with 11 against 11 we could have won the game as we were playing really well. This red card changed the game. I’m really sorry to the club, to the team and all the fans.
"I actually thought I could get the ball when I slide tackled [Harry Kane] - that is why I went for it. I touched him and [the referee] gave me the second yellow.
"But at the end of the day, it’s a good point and hopefully it will be an important point for the title."