The Reds are just three points off second-place after Saturday's win over Luton Town coupled with other results.
"It is important to remember that they (Carlisle and Doncaster) are suddenly in the spotlight now," said Calderwood.
"The effect on their results is there to see."
The City Ground boss added: "We have gained on the teams above us, we can't hide from that fact.
"Now we do not want a team to fall over the finishing line. We want to make the other sides have to win promotion.
"We have to make them win matches. We need to do our job."