Pardew is serving a seven-game Football Association suspension, the first three a stadium ban, and has been fined a total of £160,000 for the incident at the KC Stadium earlier this month.
However, owner Mike Ashley decided to stick with him and Pardew has revealed his gratitude to the sportswear tycoon, the club and its fans for their response to his misdemeanour.
Writing in his programme notes ahead of Saturday's Premier League fixture against Crystal Palace, he said: "It will always be an incident that I deeply regret and there is nothing I can do to take back what happened.
"The price I am paying for my indiscretion is heavy and I will feel it this afternoon as a massive occasion takes place at St James' Park against my former club Crystal Palace, and I will be elsewhere.
"I would again like to thank Mike Ashley, the board, my staff at the training ground, the Newcastle players and everyone at the club for their support in the last few weeks and in addition, can I express my appreciation to all of you who have written to me expressing your support at a time when I very much needed it.
"We all make mistakes in life and I have received messages from a huge number of Newcastle supporters, which have been very welcome during what has been a difficult period for me personally."