Cooper said he sensed that his side, sitting three points off the drop zone with two games left, were coming good at just the right time as they jostle with Leeds United, Everton and Leicester City to avoid an immediate return to the Championship.
Southampton were relegated on Saturday after losing 2-0 at home to Fulham.
"I’ve never had to question the resilience, the desire, the attitude, that part of the mentality," Cooper told reporters.
"At times a little bit of belief, a bit of concentration and a bit of confidence away from home - that’s why... sometimes we’ve had what we’ve had. It was good after going 2-1 down to get something out of the game."
After snatching the lead with a Taiwo Awoniyi header in the 13th minute, Forest found themselves losing 2-1 after a quick second-half brace by Chelsea's Raheem Sterling. But they bounced back quickly when Awoniyi scored another header in the 62nd minute.
Forest host Arsenal next Saturday and visit Crystal Palace away in their final game of the season while Leeds, three points behind Cooper's men and just inside the relegation zone, travel to West Ham United before hosting Tottenham Hotspur.
Everton, two points behind Forest, play Manchester City on Sunday before visiting Wolverhampton Wanderers and hosting Bournemouth. Leicester play Liverpool on Monday and then travel to Newcastle United and host West Ham.
Cooper said he would not worry immediately about the Arsenal game and would instead keep his side's training routine going as normal.
"We have got to stick to what we believe in, stick to the plan," he said. "We will go straight back to the training ground and not just focus on next Saturday too much. We've just got to focus on the next day and get as much out of it as we can."
Interim Chelsea coach Frank Lampard, who has steered the Blues to victory in only one of the eight matches in all competitions since he replaced Graham Potter in early April, lamented his side's lack of a cutting edge.
"You need to be killers at the top end of the pitch," Lampard said. "At the moment, we don’t have enough of that."
Chelsea are marooned in 11th place in the table and heading for one of their worst finishes since the launch of the Premier League, despite the huge outlay on players made by their US owners who bought the club a year ago.
Influential midfielder N'Golo Kante, absent for much of this season with injuries, could miss Chelsea's last three games - Manchester City and Manchester United away followed by Newcastle at home - after hurting his groin during training, Lampard said.
