Adkins was appointed manager of the South Coast club on Sunday night, ending a protracted exit from Glanford Park that had lasted the best part of a week.
He took charge of training at Southampton on Monday and Tuesday, with his first match coming against the parochial Dons found his new side in the relegation zone.
They remained there after the final whistle, as goals from Angelo Balanta and Peter Leven condemned the Saints to a 2-0 loss at stadium: mk. Saints are 36 places below Scunthorpe in the pyramid structure.
"There's a lot that we need to improve on, but the important thing is I've now had a game to see how the players react, to see how they respond and prepare themselves for a game and when they're up against it. The pressure's now on to see how they do react to it," said Adkins.
"So there's a lot of information that we've gained that we can learn from and keep improving to make sure this team and football club keep moving in the right direction and we do it together as one. We're on the back of four very disappointing results, we're at the wrong end of the table, but it's a fresh start for everybody in respect of where we're going to go in the future.
"We've got to address that and address it as quickly as possible. I can reflect upon this and make some good decisions on what I've got to do with the group of players I've got and whether we've got to bring players in to improve."