Real Madrid earned a victory against Rayo Vallecano, but it was far from convincing as Karim Benzema and Cristiano Ronaldo scored in a 2-0 result after the match was postponed to Monday due to a lighting failure.
Benzema opened the scoring in the 13th minute, finding the back of the net and with it getting a much-needed goal, off a pass from Angel Di Maria.
Madrid never really looked like the dominating team of last year, needing a penalty from Ronaldo with 20 minutes remaining to seal all three points and take them to seventh in the standings with seven points from five games. Ronaldo nearly got a second late on, but saw his shot come off the post.
The win leaves the defending champions eight points behind bitter rivals Barcelona, who are yet to drop a single point this season.
"If we had played with a similar attitude against Getafe and Sevilla (as we had tonight) we would have won those games," Mourinho told reporters.
"It was a tough game, a difficult game and we had to be at the least at our best in terms of concentration and motivation and it seems that the team responded well in that sense.
"Could we have played better? Yes, we could have played better even though our opponent pressured a lot and ran a lot and caused us problems.
"But my criticisms are always directed at my players' attitude and whether they are committed to the game and today the team was a team."
Mourinho admitted it was not ideal to see the game postponed to Monday. "It was not an easy situation for us, but it was not easy for them too," the Real manager said. "You come with the mentality to play, wait but are then forced to wait and wait for confirmation, and you don't play."
Real striker Gonzalo Higuain insisted there was plenty of time to catch up with Barcelona. "It was an important game. We came here on the back of a large gap behind Barcelona and had the intention of getting the three points. It was very difficult," he said.
"Must we treat all of our remaining games as finals? We're at the fifth matchday, there is still much to play for. The distance is important but plenty more matches ahead. 33 games is an eternity and we're going to fight until the end.
"At times, we seemed akin to the Real Madrid of last season, but we did not take advantage of all the chances we created. The penalty was good for us, along with the red card.
"I think the team were good overall. We still have room for improvement but we started well in the Champions League, that's a fact."
In Monday's other match, two late goals helped Sevilla to a 2-0 victory over Deportivo La Coruna. Alvaro Negredo struck from close-range in the 75th minute, before Ivan Rakitic made the game safe seven minutes from time.
