Forest still trail the table-topping Iron by 10 points, though that could be reduced to seven when they host Doncaster in a rearranged game on Tuesday.
And Calderwood wants his side to string together a run of results to pull away from the chasing pack - with teams like Bristol City, Oldham and Yeovil all continuing to drop points.
"Scunthorpe have done remarkably well, but we know that if we can put a run together now it could put us clear of the other teams near us," he said.
"Our last couple of results have reflected not only what we have done on the field but the way we have been on the training ground and it is important that we continue to move forward in the coming weeks
"We've gone back into second place in the table and it's up to us to try and stay there at a time when we have difficult games coming up this coming week against Doncaster and Scunthorpe. "