One player to benefit was Jonathan Forte, who came into the side for a rare start. He scored with just four minutes on the clock.
"We changed our formation to be a bit more defensive and to give ourselves a chance going forward. With the players we have, we can score goals," said Adkins.
"It was great character from the players. We are newly promoted and have had some difficult results away from home. We lost 4-0 twice and had not managed to score.
"I was delighted to keep a clean sheet. It's the first time since pre-season that we have been able to work defensively as a back four. I've not had the defence that I wanted."
Goals from Paul Hayes, Sam Togwell and Martin O'Connor in the second-half ensured a win that was the most impressive result of the day in the Championship.
Neil Warnock, the Palace manager, felt his side had made it far too easy for the visitors.
"I don't think Scunthorpe have scored a good goal. I'm not knocking them, we absolutely put it on a plate for them. They must think they won the pools," he said.
"We can't play like that. All you can do is apologise to the fans who I thought were terrific. I would crucify the manager if I was one of them after that."