The 31-year-old opened the scoring and teed up Romelu Lukaku for the second before he was dismissed for pushing Gaston Ramirez in the face after he elbowed Shane Long.
Fortune has now apologised for his angry reaction, which will see him suspended for three of the last four matches of the season.
"We won 3-0 and I scored and got an assist so it was a good game for me and for West Brom, but afterwards I know everyone will talk about my red card," said Fortune.
"First of all I want to apologise because I don't usually do that. People know I'm not a bad guy so I am really frustrated but I just reacted to what the Southampton guy did."
Fortune will be out of contract in the summer, but he hopes manager Steve Clarke will want to extend his three-year stay at The Hawthorns.
"For the moment I am still waiting for something from the club," he added. "The fans ask me on Facebook or other social media but I always answer that I would be really pleased to stay here and I am just waiting for the offer from the club.
"Now it is up to them and I am still waiting. I talked with the manager and I said if he doesn't want that to be my last game they have to sign me. I think I have done well in my three years here so we will see what happens.
"They know my position. I want to stay and if the club want me to stay we will have to discuss it, but it is up to the club."