The 48-year-old was replaced by Mauricio Pochettino in January despite having led the Saints to back-to-back promotions from League One to the Premier League.
But, following his unveiling with the Royals, Adkins has revealed he doesn't bear any grudges over his dismissal.
"I've not made any comments since I left Southampton and I want to take the opportunity to thank all the people there," he told reporters. "I thank the fans, the players and supporters. We were on a fantastic journey but we have to move on now."
He added, "I am pleased to be the Reading manager. We will take it one game at a time and try and keep this club in the Premier League. It's a good club, I've been impressed with them and I've always known what sort of club it is. We're in the Premier League and we want to stay there. I am excited."
Adkins will come up against his former club in his second game in charge but says he is only concerned with preparing Reading for their trip to Arsenal on Saturday.
"I can't talk about Southampton as it's in the hands of the League Managers' Association," he explained. "It's one game at a time and the next one is Arsenal. I am looking to the future, I've had two months out and gone around Europe, I'm excited about the future and passionate about playing football.
"We all have to pull in the same direction and it is a great challenge."