The 48-year-old coach will face the Saints for the first time this weekend since he was dismissed as manager, despite having led them to back-to-back promotions to the top tier of English football.
And Adkins insists that the pieces were in place for his old club to retain their Premier League status, with the team losing just one game in its last twelve prior to his sacking.
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"We knew that we had a periodised training programme and we were going to get fitter and fitter as the season went on, and that has proved to be the case."
"We knew we had good players and we were on a good run, just two defeats in 12."
Meanwhile, Adkins' replacement Mauricio Pochettino says he does not feel guilty over the manner in which he was appointed, adding that he fully respects the work of his predecessor.
"I didn't feel bad at all," Pochettino said.
"From the first moment, I felt I was treated very well. I felt I was part of a family, part of a club with an amazing work ethic so that has made me very happy. I felt really comfortable from the beginning.
"Nigel has my full respect for the job that he did here. As well as him, there are a lot of people behind the scenes that are responsible for the club being in the Premier League and doing so well in the past two or three years."