Chelsea moved up to second in the Premier League with a 2-1 victory, but resurgent Palace gave a good account of themselves.
Goals from Fernando Torres and Ramires sealed the points, with in-form striker Marouane Chamakh equalising for Palace in a frantic London derby.
Palace had won their previous two games to raise hopes of avoiding relegation and Tony Pulis' team had plenty of chances to secure at least a point.
Mourinho was left to rue Chelsea's inability to reward their dominance with a victory against Pulis' former club Stoke City last weekend and the former Real Madrid manager was relieved to cling on to all three points against Palace.
"It was tense. We had a lot of chances to kill the game but we didn't," he told Sky Sports News.
"It is three very important points against a team with fantastic spirit and very well organised, playing the way Tony Pulis wants.
"They were a difficult opponent for us and difficult opponents for any other club."
Victory for Chelsea ensured Mourinho's side cut the gap to leaders Arsenal by only two points ahead of next Monday's Premier League clash between the two title rivals.
