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Flower became the first player to be shown a red card during Super League's season finale when he twice punched Lance Hohaia in the second minute of the clash that St Helens won 14-6.
The incident has sparked much outrage - Hohaia was flat on his back on the floor when the second punch was thrown - with many calling for Flower to be handed a lengthy suspension.
Flower has since said sorry to Hohaia, Saints and the sport in general, admitting there is "no defence" for the incident.
"I am so sorry for what happened," he said in a statement issued by Wigan on Sunday.
"There is no defence for my actions.
"It is something that happened in the heat of the moment. I instantly regretted it and am devastated that I allowed myself to punch someone like this.
"At Wigan we are known for being aggressive but we are constantly told to do this within the rules of the game and that punching isn't tough. We may aim to dominate teams, but we don't aim to hurt people.
"I firstly offer my apologies to Lance. I have full respect for him and have never gone onto a rugby field to injure a fellow player. I hope he is ok.
"I'd also like to say sorry to my team-mates, our fans and Wigan. I know I've let them down like never before and accept I'll have to live with this for the rest of my career.
"Finally, I'm sorry to the sport of rugby league. It was a big night and I know I've taken attention away from a special event."
Wigan chairman Ian Lenagan and coach Shaun Wane said jointly: "We apologise unreservedly, on behalf of the Wigan club, to Lance Hohaia, St Helens and the general rugby league family for Ben Flower’s totally inappropriate behaviour.
"Rugby league is a tough sport, which we are proud of, but such a response is neither encouraged nor condoned. Such behaviour is not representative of rugby league nor the Wigan club."
Hohaia, who missed the remainder of the game, bears no ill-will towards Flower and is set for a scan to determine whether or not his nose was broken in the unsavoury incident.
"Sometimes these things happen in a game, in the heat of the moment people do things they regret," said Hohaia, a World Cup winner with New Zealand in 2008.
"I've done some silly things myself, so I don't hold any regrets against Ben.
"I don't remember the incident – people have been telling me what happened."