"It's imperative that the club stays in the Championship and we need to give ourselves every opportunity to do that."
Forest are currently one point adrift of safety in the Championship, in 22nd place, having won just four times in 25 games.
Speaking immediately after the game, Calderwood was asked whether he felt that the defeat would spell the end of his time in charge.
"No," he said. "But it was a real bad day. It was a poor performance.
"We were poor with the ball and hopeless without it."
It felt like the end for Calderwood. It was the kind of performance that gets managers the sack. There are bound to be calls for the likes of Roy Keane and Stuart Pearce to take charge - whoever it is, it's imperative they keep the club in the Championship"
BBC Radio Nottingham's Forest correspondent Colin Fray
Calderwood was appointed as Forest boss in the summer of 2006 after winning promotion from League Two with Northampton Town the previous season.
He almost won promotion at his first attempt. But, after Forest led the table for the first half of the 2006/07 season, they faded to finish only in the League One play-offs.
Then, after earning a 2-0 first-leg lead at Yeovil, they imploded even more spectacularly, bowing out with a 5-2 second leg defeat in front of their own stunned fans at the City Ground.
They atoned in May when they came from the play-off pack to claim second place on the final day of the season - and automatic promotion.
But Calderwood's young Reds have struggled to adapt to life in the Championship - and the Boxing Day hammering to bottom club Doncaster (they were four down in little over an hour before a late rally) was their 12th defeat in 25 league games, only four of which they have won.
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