Flower was dismissed with just two minutes on the clock at Old Trafford before the Warriors were beaten 14-6 by their bitter rivals.
After receiving widespread condemnation for his actions, the 26-year-old has now said sorry for the incident.
"I am so sorry for what happened last night," he said in an official statement. "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 may aim to dominate teams, but we don't aim to hurt people. I firstly offer my apologies to Lance. I hope he is okay. I'd also like to say sorry to my teammates, our fans and the Wigan club. I 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."