"To say I'm delighted is an understatement," said Adkins, after watching United compete well on their return to the second tier after a 43-year absence.
"A few years ago we were staring into the abyss of the Conference and we've turned it around.
"It's a big step-up and has taken us 43 years. We are clear favourites to get relegated, and Charlton were clear favourites to win this game.
"But it just goes to show on any given day that anything is possible."
Charlton boss Alan Pardew also paid tribute to the Iron, although he felt poor marking contributed to Scunthorpe's equaliser.
"I thought Scunthorpe were brilliant. They were fighting for their lives and put themselves on the line. For all of our quality we couldn't see them off," said Pardew.
"Offensively we did well and should probably have got another couple of goals. And after we scored we got a little bit sloppy.
"I think Marcus was probably still celebrating his 100th goal and let his man go. But he's held his hands up in the dressing room, as he should do."