The midfielder was sent off after 66 minutes of Tuesday night's third-round loss at Fratton Park for showing dissent towards referee Fred Graham.
Pompey managed to score despite their numerical disadvantage, but Liam Lawrence's strike eight minutes from time was too little, too late after Michael Morrison and Lloyd Dyer had put Leicester in control in the first half.
Cotterill said: "What do you want me to do, cane him?
"I could go up the wall and I could slaughter him, or I could ask him what he said, which I did, to which he said 'I'm sorry to all the lads, I've let you all down and I was wrong to do it.'
"What more can you say? He apologised because he is a decent lad, he is a really decent lad. Anyone who knows Richard would know that.
"But I am not surprised the referee sent someone off and I am not surprised it was one of our players, especially given how he was talking to them.
"Richard has been sent off for foul and abusive language, which we wouldn't condone anyway. But I am certainly not surprised he sent one of our lads off. The game was all about him if I am honest."
The two goalscorers for Leicester, along with Andy King, were the only survivors from the side that started the league defeat to QPR at the weekend as boss Paulo Sousa made eight changes.
The Portuguese defended his policy of making wholesale changes in the cup, and praised the first-half performance of his players.
"We can change players and make rotations in this type of game," said Sousa.
"I am glad to make rotations with the squad in these games because I can understand the level of players who don't play so often. I can understand how they can help to improve our team straight away.
"I always want my players to go into the games with a winning mentality. Winning always encourages everyone and motivates us to do the right things.
"Since the international break, we have made a huge improvement. We want to keep up that standard for the rest of the season and improve in every game.
"The first 45 minutes were the basis of what we did. We started quick with a high tempo. We were well-organised defensively and always had the right attitude to win the challenges.
"We made good decisions whether to keep possession or move quickly to our offensive moves. We scored two goals and we could have scored a few more. However, we had a few mistakes and I expected a little bit more in the second half."