Palace opened the scoring through Glenn Murray, who bundled home after eight minutes but Forest levelled on the stroke of half-time thanks to Andy Reid's superb finish from 25 yards.
Murray restored the advantage with nine minutes remaining with a precision, looping header, but Billy Sharp had the final say in added time, tapping in after his shot struck a post.
"I thought there was a lot of fighting spirit among the players. To their credit they went all the way to the final whistle", McLeish said.
"They could easily have put their heads down after Palace had taken the lead again in the last 10 minutes but they fought right to the death and that shows great character.
"I also saw some great quality on the field. Andy Reid was fantastic - what a game he had, and he was instrumental in the two goals. The one he scored was a peach."
McLeish, who took charge of his first game following the sacking of Sean O'Driscoll, thanked the City Ground for getting behind the team.
"Even when we went behind late on there was a great response from us and I was delighted with the crowd too. They appreciated what the players were doing and I think the excitement they created gave the fans the impetus to roar us on."