"We have a very disappointed dressing room," said Adkins, who has now overseen five first-team matches for the club.
"We have enjoyed some big third round ties in the past few seasons and wanted to be there again.
We felt this was a game we could win, but we could not final the quality in the final third that we have shown all season.
"Take nothing away from Wrexham they worked very hard for their victory."
Wrexham boss Denis Smith reckons his side could have performed even better.
"I am not a betting man but when I saw the odds were 5-1 against us winning, even I was tempted to have a flutter," he said.
"We have beaten a very good side. I was impressed with Scunthorpe, even today.
"They have the best two strikers outside the Championship in Sharp and Andy Keogh, but my two centre halves kept them quiet.
"To come here and win 2-0 is an excellent performance but I know we can still play even better
"We have beaten a very good side. I was impressed with Scunthorpe, even today.
"They have the best two strikers outside the Championship in Sharp and Andy Keogh, but my two centre halves kept them quiet.
"To come here and win 2-0 is an excellent performance but I know we can still play even better