McLeish was relieved to grab a share of the spoils when Billy Sharp scored in stoppage time at the City Ground.
And the Scot singled out Andy Reid for praise after he scored one goal and set up the equaliser.
"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 today. Andy Reid was fantastic - what a game he had, and he was instrumental in the two goals. The one he scored was a peach."