Adkins was dismissed by Southampton in January after leading the club to back-to-back promotions, but has returned to management after replacing Brian McDermott at the Madejski Stadium.
Reading are seven points from safety, with just eight games remaining, and Adkins is looking forward to a new challenge.
"I've not made any comments since I left Southampton and I want to take the opportunity to thank all the people there," Adkins told a press conference on Sky Sports News.
"I thank the fans, the players and supporters. We were on a fantastic journey but we have to move on now.
"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."
Southampton will be Adkins' second opponents as Reading manager, but he would prefer to focus on his first game in charge away to Arsenal on Saturday.
"I can't talk about Southampton as it's in the hands of the League Managers' Association," he added.
"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."
Brighton & Hove Albion manager Gus Poyet turned down the chance to take charge at Reading amid reports that Adkins was not thought to be interested.
Adkins addressed that, though, saying: "When it happened with Brian I was in Germany and Reading wasn't on the agenda at the time.
"We're now looking forward to the next stage together."