Cisse on Tuesday accepted a Football Association charge of violent conduct for the altercation, which occurred during the Magpies' 3-2 Barclays Premiers League win on Sunday.
The 29-year-old Senegal international, who has now played his last game for the club before heading to Equatorial Guinea for the African Nations Cup, insists the incident was totally out of character.
"I'm sorry for doing something like this," he told club website nufc.co.uk. "I'm not the sort of player who does something like this.
"It is 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 will miss Thursday's match against Burnley at St James' Park, Saturday's FA Cup tie at Leicester and the January 10 trip to Chelsea.