The rattling the woodwork twice as Crewe struggled to hold on, with Paul Hayes and Izzy Iriekpen adding gloss to the victory.
"In the first half our passing was not at the standard we want it to be" said Adkins.
"But in the second half some of our play was a joy to watch, we played some really exciting football.
"There is so much more for us to get out of this team. Somebody is going to get a good pasting from us."
United overtook Leicester City at the top of the table thanks to this win, although it is only thanks to goal difference and the Foxes have a game in hand.
"It was great to give our fans a chance to sing. We had honestly not talked about it before the game - but we have no problems being top so early in the season," added Adkins.
"Two years ago we went top at the beginning of January and went on to win the League One title.
"The important thing though is to be top of the table at the end of the season."
The Crewe coach Steve Holland concede his side had been well beaten.
"I thought the first half was fairly even but then we have conceded a feeble goal when Billy [Jones]gave the ball away cheaply by lobbing it aimlesly into the centre of midfield and Hayes has been allowed to cross into the box for a tap-in," he said.
"We didn't threaten enough either, our best chance saw Tom Pope have a header tipped over the bar. It was a fantastic save just before half time. I wouldn't say it could have been a turning point because Scunthorpe put us under a lot of pressure after the hour.
"We started the second half well enough and then we started to lose concentration and gaps started to appear.I don't know if it is a physical or mental thing. I know that we cannot do any more fitness wise and that is a fact, so we will have to look at their menta capabilites."