Caolan Lavery opened the scoring for United after 35 minutes played, before a goal in each half from Spireites forward Joe Quigley ensured the points returned to Derbyshire with the visitors.
Speaking to Iron Player post-match, Nelson was quick to share his disappointment, stating: "On the balance of it, you look at the chances we had, we should have had more than one. Chesterfield can probably say the same they've hit the post a couple of times.
"I think we have had some equally as good chances as well. I am very disappointed that the result is decided on a real poor goal on our part.
"We probably need to be a little bit more disciplined in the first half and get in at 1-0. Then you look at the goal we give away after half time and the timing of it, we make a mistake giving the ball away and they go and punish us.
"[I am] Really disappointed but gutted for the lads as they have put in another good performance against a real top quality side. We probably should have come away with something."
With Scunthorpe having to deal with injuries to both Rob Apter and Owen Foster during the 90 minutes at Glanford Park, Nelson provided updates on the pair.
"We will have to see," he added. "Fozzy's [Owen Foster] doesn't look good with it being a shoulder injury, we don't know how long that is going to keep him out.
"He will have to be scanned and assessed. Rob [Apter], the good thing was he tried to carry on but the decision was made to take him off and try and protect him.
"The next 24-48 hours will be decisive in order to decide whether or not he will be available for the next game.
"With Fozzy's I don't know if he did it with that great save, I thought he had dislocated his shoulder at first but the medical team have said that isn't the case, so we will have to wait and see how he is.
"Rob is one where he had just tweaked the side of his knee and hopefully it's not that bad so we can have him available for the next game."
With our next domestic action coming against the same opponents in just six days' time, the 42-year-old was keen to talk up the Iron’s chances next time out, believing there are positives to take from today’s encounter as a whole.
"I think we gave a very good account of ourselves," he added. "If we try and repeat that and cut the mistakes out then you would like to think we can get something out of the game.
"No two games are ever the same and I am expecting them to be fired up and right up for it considering they are at home. We will go with the same desire, cut out the mistakes and try to be a little bit more clinical inside their box."
Finally praising our supporters for their endeavours this afternoon, the interim boss concluded: "They stuck with the lads today and you know it was pleasing that we managed to get the goal and go ahead, it was just a shame we couldn't hold out, whether that be a draw or even better a win."
See more from Michael Nelson on Iron Player.
