Forest boss wants reaction
The have now taken just four points from the last 15 on offer, and have dropped to third in the League One table after once boasting a seven-point lead.
Clingan was sent off after a badly-timed challenge on Will Haining, while Cullip was also shown a straight red after bringing down Chris Porter in the area.
"We were 3-0 down before we even got any opportunities," admitted Calderwood.
"We will take a look at the sendings off because it gives us reason to believe that we might have won.
"But credit to Oldham, they looked clever and once they had got the first goal it was always going to be a struggle.
"Now I want to see a good reaction and I am sure the players will be positive.
"It will take a really big effort both mentally and physically in the next couple of games."