Pettersen, the world No.8 and highest-ranked European player in the women's golf rankings, sparked controversy during the Solheim Cup Sunday after refusing to concede a putt on the 17th hole of the final fourballs match.
American Alison Lee missed a putt for birdie and then scooped the ball up with her putter believing Pettersen and her teammate Charley Hull, who had started walking towards the 18th tee, had conceded the putt.
Pettersen appealed to the match referee saying she hadn't conceded the putt because it was more than three feet. The claim drew widespread criticism but under the rules the hole was awarded to Europe.
"I've never felt more gutted and truly sad about what went down Sunday on the 17th at the Solheim Cup," Pettersen said in a post on her Instagram account.
"I am so sorry for not thinking about the bigger picture in the heat of the battle and competition. I was trying my hardest for my team and put the single match and the point that could be earned ahead of sportsmanship and the game of golf itself!
"I feel like I let my team down and I am sorry."
In a sport that is well-known for its etiquette and sportsmanship, Pettersen's actions left teammate Hull and Lee in floods of tears and the Norwegian also revealed she has personally apologized to USA captain Juli Inkster.
"To the U.S. team, you guys have a great leader in Juli, who I've always looked up to and respect so much. Knowing I need to make things 'right,' I had a face-to-face chat with her before leaving Germany this morning to tell her in person how I really feel about all of this. I wanted her also to know that I am sorry.
"I hope in time the U.S. team will forgive me and know that I have learned a valuable lesson about what is truly important in this great game of golf which has given me so much in my life.
"To the fans of golf who watched the competition on TV, I am sorry for the way I carried myself. I can be so much better and being an ambassador for this great game means a lot to me."
Following the furore, Team USA went on to pull off a stunning comeback to win 14½ - 13½ and Inkster believes the feeling of injustice inspired them to turn the competition on its head.
"I think maybe that (incident) just lit the fire a little bit more," she said. "And I think in their bellies they just wanted to do a little bit more, and that little bit more got us the Solheim."
Prior to Pettersen's apology, Inkster had described the Norwegian's actions as "BS [bull***t]," while former European Solheim Cup captain Mickey Walker called it a "terrible injustice."
Pettersen, a two-time major winner, spoke to CNN in the build up to the Solheim Cup
, but nothing could have prepared her for the events that would unfold.
Despite initially appearing unrepentant about the incident -- Pettersen said she would "totally" do it again in a press conference afterwards -- the 34-year-old will be hoping she can put the controversy behind her.