The Saints were 4-0 winners over Coventry at St Mary's, to ensure they finished second in the Championship less than two years after Adkins left Glanford Park for the South Coast side.
"A lot of people put a lot of hard work in, and for the players trying to get off the pitch now, being mobbed by our fantastic supporters, they deserve all the plaudits they get. Since I joined the football club, they've been tremendous," he told the BBC.
"Everybody at this football club has worked their socks off and deserve all the praise they get.
"I'm very proud and honoured. We've put a lot of hard work in so it's good. I'm a happy man."
There is a strong Iron connection at St Mary's, with Adkins assisted by Andy Crosby in a partnership that started at Glanford Park.
The opening goal in this match was also scored by former United favourite Billy Sharp, who led the line as Adkins steered Scunthorpe to the League One title in 2007.
One less happy Iron link to Saturday's match is Joe Murphy, with the former Scunthorpe keeper forced to pick the ball out of his net four times as he kept goal for Coventry.