For Adkins, though, getting back to winning ways - after losing to Oldham Athletic and drawing with Swindon Town in League One - was more important than the performance.
"Credit to Rochdale, they are a good outfit and it was a battle for us," he said.
"We are a good footballing side but they denied us the right to play. There weren't many scoring opportunities for either side and right at the death we have gone and got the winner from a set-play.
"So we are pleased with that, we are also pleased with a clean sheet at the back - we looked solid."
The Rochdale boss Keith Hill found defeat hard to take after conceding such a late goal, but said his side could take a lot of credit from their display.
"Performance-wise I have nothing but praise for my players. They were superb," he said.
"Scunthorpe are currently the best team in League One and yet they have had to change formation to nullify our threat.
"We have got to take that as a great compliment and on another day it could so easily have been us going through to the next round."