The Crystal Palace boss was hit with the charge following his behaviour at the full-time whistle of his side's 2-2 draw with Leeds last weekend.
He was given until 4pm on Friday to respond but he revealed he will not be appealing.
"It's a waste of time taking on the judge and the jury, so I won't be taking them on," he told the club's official website.
"What's the point? You have to look at your behaviour and I was shouting (while) walking on. I got my players off but I was shouting and I have to be some sort of role model.
"It's very, very difficult at times. It's a chain of events really and I've never been very nice when I don't get what I want - and I didn't get what I wanted."
Palace winger Wilfried Zaha was also charged for improper conduct in the same game.
Holloway added: "(It) was a silly thing to do, and then he put something on Twitter which is also a silly thing to do. We're all human beings trying to get on and the game itself is much bigger, we've got to try and show the public the right image.
"He's a young man who's had a tough year where he has gone from being a good player to a sensational player and is now in the spotlight. That's not easy to handle but he'll learn and bounce back.
"Why should they ban him? I don't get it, trying to hurt someone in a tackle is worse and that should be looked at. What's more dangerous, a gesture or trying to elbow somebody?"
- Sports & Recreation