Aaron Rowe and Juninho Bacuna scored either side of half time to help the Terriers win for just the third time in 20 league games.
The result moved Huddersfield to 18th, eight points clear of third-bottom Rotherham United, with four games to play. The Millers do have three games in hand, however, meaning there is no room for Town to relax just yet.
Nottingham started the game on top but Corberan explained how a tactical switch with his forwards allowed his side to get a foothold in the contest.
"We changed Aaron Rowe and Duane Holmes around, I think it helped the team win a bit of time with the ball in the offensive half," he said.
"In the second half, we made sure we didn't try and make sure the game would be over quickly.
"We created some options in attack but it is difficult when you need a result sometimes you don't do the things you need to, you just want the game to end.
"But I think we had some good options on the counter-attack and on of them Bacuna scored a very good goal.
"We had to put in an unbelievable effort in defence because I know the quality of Nottingham Forest Without the level of effort and team spirit, it would have been impossible to get something positive today."
Corberan was in no mood to take credit for the result, quickly putting all the praise onto his players at full time.
Huddersfield took the lead as Rowe pounced on a loose pass late in the first half before Bacuna doubled the lead with a thunderous second-half strike.
He added: "Everything we did on the pitch today arrived from the players.
"After a few difficult minutes at the beginning of the game, the team started to find a way to compete better.
"I think, as the minutes passed we became more concentrated and defended better. We were able to use their mistake for the first goal."
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