Oscar's close-range strike and Jon Obi Mikel's first ever Premier League goal ensured the Blues ended a forgettable week on a high note.
Mourinho's men lost at Everton last week and then slumped to defeat in the Champions league against Basle at midweek, meaning the pressure was on Chelsea on Saturday.
While they were rarely stretched against their London rivals, Mourinho thought they played better in defeat at Everton.
"The result was better than the result against Everton," he said on Sky Sports 1.
"I still think that they played much better against Everton than the did today [Saturday] but points are also important after a bad start - a start that everybody keeps telling me is the worst start in about a decade.
"But today [Saturday] I could go to bed and I look at the table and nobody is in front of us."
Mourinho has not been too dispirited by Chelsea's struggles at the beginning of his second spell at Stamford Bridge although he added he needs time in order to make his mark.
"I'm in football for a long time and I'm not expecting when the results are not good, people to speak well about our work and about our team," he added.
"I also think my career is made of this, other people have and deserve time, other people can not win one, two, three, four, five years and they keep having a peaceful life and won't get in any kind of pressure.
"With me, maybe because normally I win in the first season, people demand a lot and don't understand I'm building a different team.
"The most difficult thing is first of all to change the philosophy and that takes a little time.
"I understand at this moment we are not playing very, very well, the results are not especially good.
"But the beauty of the Premier League is that in other championships, and I've played some of them, when one of the big teams lose a match, it is catastrophic because nobody loses points and they win, win, win.
"The difference of the Premier League is that everybody loses matches, everybody loses points, the six top teams have already had a defeat so no dramas."
Mourinho added: "I have to say I have never worked so hard as I have done this season with this group of players and I trust in the future and in relation to critics' opinion, I learn for a long time to respect that."
Mikel's first strike in his eighth Premier League season sealed victory for the Blues on Saturday and the Nigerian was relieved they managed to end a four-match winless run.
"It was good but I think today's game was all about winning," he said.
"We lost two games in a row and the most important thing today was to win the game and I'm glad we did that, got the three points and my goal is just a bonus.
"I'm really happy, it's been a long time, the guys have been killing me about it. They say 'you go to the national team and you score but you don't score for Chelsea.
"It's good for me to get a goal here."
Oscar put them on their way in the 52nd minute to cap a man of the match performance from the Brazilian.
He added: "I'm very happy. A win is very important for us."