The Senegal international lashed out in Coleman's direction multiple times at a corner during Newcastle's 3-2 victory at St James' Park on Sunday, although he was not punished at the time as referee Craig Pawson did not see the incident.
However, Cisse was charged and subsequently banned by the Football Association, meaning he will miss Premier League games with Burnley and Chelsea, plus the FA Cup third-round tie with Leicester City.
Speaking to the club's official website Cisse apologised for his actions, and accepted that the FA was right to ban him retrospectively.
"I'm sorry for doing this," said the striker. "I'm not the sort of player who does something like this.
"It's not like me, I am not an aggressive player but in football you cannot do something like this. I would like to play in the next games but I did something that is not good and the FA were right to ban me.
"I would have liked to play against Burnley, to help us get a win, but I am sure the other players will do well and win the game for us.
"We need points and need to win and it is not an easy match. I will not be on the pitch but my head and my heart will be with the team for the game."
Cisse is unlikely feature for Newcastle until February at the earliest due to the ban and his participation in the Africa Cup of Nations with Senegal.
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