Derby suffered another disappointing performance and defeat as they fell 2-0 against Wolves last Friday, which has left the side clinging onto the pack near the top of the Championship table.
However, despite trailing Watford by five points and Bournemouth by six points, Grant feels that a top two position is still possible.
“It would be wrong for us to give up on automatic promotion. We've shown we're capable of winning two, three, four, five games on the spin,” he said.
“I think it would be wrong for us to give up or for anyone to write us off – but we expect them to.”
Grant does have a point in the respect that at one point in the last few weeks, the side were top of the table with a small cushion.
They are capable of getting themselves into a good position at the top of the table and producing the form required to get there.
However, games are running out and other sides are showing great form and momentum at the moment to hold positions above Derby in the table.
Steve McClaren’s team face a big challenge, with a squad carrying several injuries, to fight their way into one of the top two positions.
The international break probably comes at a good time for the Rams because they have a chance to rest and get those injured players back, as well as working on the tactics and changing things up after a poor run.