Radek Cerny, keeping goal at the opposite end of the pitch, was only tested by a shot from Grant McCann. Other than that the Czech keeper enjoyed a quiet afternoon.
"We paid the penalty for a slow start. That was just what we did not want," said Adkins.
"Wehad a couple of players who switched off, did not do their jobs, and we were a goal behind. It's difficult to come back from that sort of thing at Championship level and that is a lesson we have got to learn.
"We pressed strongly for an equaliser but in truth we did not test their goalkeeper often enough and that is down to Rangers' defence who produced several good blocks to deny us."
The win was the visitors' first in the league this season. Jim Magilton, the Hoops' manager, felt his side should have sealed the game with a second goal.
"We got a bit nervous towards the end but we're finally up and running and that's important," he said.
"I thought we started here as brightly as we have started any game this season. I thought the quality of our play in the first 10 to 15 minutes was very good.
"But I did then think that we took our foot off the pedal and allowed Scunthorpe back into the game. This is a difficult enough place to come to without offering them that opportunity."