The Wirrall side moved a point behind the Iron with a 2-0 home win over Bristol Rovers on Sunday, doubling the misery on Nigel Adkins as they lost the Johnstone's Paint Trophy final to Luton Town.
United have eight games to play compard to Tranmere's six, making Scunthorpe clear favourites to hold on to a top six place.
But Moore is keen to make the Iron work as hard as possible to ensure a place in the end-of-season promotion lottery.
"We've got to try and put that little bit more pressure on Scunthorpe now. Let's see how they react after losing the Johnstone's Paint Trophy final," he said.
"That may have taken something out of them physically and mentally, but it's up to us to keep on winning.
"We want to put pressure on Leeds in fifth place as well as Scunthorpe and it may come down to who wants it most."