He said: "This was a polished display and we kept another clean sheet. We defended well, we didn't think Chesterfield would relish coming here.
"We are willing to take on anybody at home because we make it tough for them.
"It took two great goals to win the game, the first was text book stuff we'd been working on all week and Ian Barraclough's strike was quite exquisite.
"This result means we can now stay over next Friday night in preparation for an important game against Bristol Rovers."
His opposite number Roy McFarland admitted the best side won.
He said: "We lacked passion and it's disappointing from a financial point of view.
"We didn't deserve to win the game, we defended too deeply at times, allowing Scunthorpe's two central mid-fielders to run the show and their front two were always dangerous.
"We did okay in the first half, but this is a poor result and I'm very disappointed."
The draw for the second round takes place on Sunday at approximately 4pm, it will be shown live on BBC 1. The full draw will be on Iron-Bru.net shortly afterwards.