United secured three points with a wonderful injury time winner from Nemanja Matic - who hit the ball on the half volley from 30 yards - but an inept first half display meant Mourinho's side had to do things the hard way. A deflected Andros Townsend shot and an early second half strike from Patrick van Aanholt had put Palace firmly in control.
However, goals from Chris Smalling and Romelu Lukaku drew the game level, before Matic's late strike secured the points.
Speaking to Sky Sports, Mourinho said on the victory: "(It was) a difficult match for me because my team made so many mistakes. We had amazing attitude and very good quality football in the second half but we made so many defensive mistakes.
"I don’t like my teams to lose organisation like we did, but an amazing match and amazing comeback, and very important victory for us because now we have nine matches to the end and we have nine points to fifth place which is not amazing but is OK."
After finding themselves 1-0 down at half-time, Mourinho claimed that he could not share what he said to his team during the break: "I cannot tell you half of the things I told my team at half-time because there would be lots of bleeping on television."
Mourinho did not get the immediate response he would have been looking for, as Palace doubled their lead within minutes of the second half kicking off. But he was happy with how his side responded and turned the game around.
He added: "Disgraceful, childish, you can find so many objectives for the second goal, everything changed, but then the players kept an amazing attitude. To come back from 2-0 down away from home against a team that is desperate for points, it gives us a great feeling."
Mourinho gave credit to Crystal Palace and Roy Hodgson as he praised his opposing manager for the way he set his team up.
"I have to say that Roy had a fantastic gameplan, really aggressive, two big strong strikers to play direct to them and cause us problems with crosses and direct football and second balls, also counter-attacking with Townsend and Patrick.
"So sometimes the winner is the one that deserves congrats but I have been many times on the losing side and sometimes I felt I did many things right and I think Roy did everything right."