Real needed a stellar display from their goalkeeper and captain Iker Casillas to net the three points at the Vicente Calderon after first half goals from Karim Benzema and Mesut Ozil had put them 2-0 up.
It was a second big game in four days for Madrid, having beaten Lyon 3-0 on Wednesday to reach the quarter-finals of the Champions League, and Portuguese boss Mourinho admitted his stars needed a rest.
"They (Atletico) had a week to prepare for the duel and us, two days," said Mourinho. "The team was tired. I was also tired and I'm the coach. The second half was difficult. We couldn't hit them on the counter-attack.
"We defended as well as possible and we achieved an important derby win. They are all tired, physically and mentally."
Real are still fighting for three trophies having reached the King's Cup final, Champions League quarter-final and they continue to try and catch Barcelona in the title race.
Spain captain Casillas was the undoubted man of the match for Real with four or five terrific stops and Mourinho heaped praise on his skipper.
"(Iker) Casillas has done a fantastic job. I like it when my goalkeeper doesn't have much to do in a game, and he had a lot to do and he was fantastic," said Mourinho.
"Atletico have shown their great spirit and quality of play, and Madrid had an answer to those who thought that the league finished today.
"I was very worried (about an equaliser), but at the same time I was full of trust in the players' mentality and fighting spirit. I know football and many things happen in the last minutes and change the result. But they fought, they gave everything and I'm pleased for the players."
One black spot for Madrid was the injury to Cristiano Ronaldo with the Portuguese winger, who has only just returned from a thigh injury, hobbling off with a hamstring injury that is expected to sideline him for two to three weeks.
"I would like to have rested him (Ronaldo), but I didn't want the championship to end today and Cristiano Ronaldo is very important to us," Mourinho explained. "It was a risk to play him, but you need to live day to day."
Real trail pacesetters Barcelona by five points with nine games left to play although one is the second 'El Clasico' between the two sides at the Santiago Bernaebeu on the weekend April 16/17.
"It was fundamental that we won to stay alive in the title race," said Real defender Ricardo Carvalho. "If we want to win the title we are going to have to win all the remaining games."