The 2012 European champions were always in control at Stamford Bridge but only had Eden Hazard's first-half goal to show for their superiority.
"They kill me every game," said a smiling Mourinho after Chelsea climbed to third in the Premier League, two points behind leaders Arsenal.
"Every game I am tired at the end. At halftime we should all be relaxed with a comfortable score but time goes on, we didn't score the second goal and you feel the opponent is keen to risk a bit more and put in a second striker and you are a bit in trouble," he told a news conference.
"But the boys worked hard defensively and in the last part they looked comfortable and we had control of the game so it was a deserved victory and an important victory."
Mourinho, who has bemoaned the lack of goals from his misfiring strikers all season, said German goalkeeper Gerhard Tremmel was the reason why Chelsea did not produce a more emphatic scoreline.
Samuel Eto'o was preferred to Fernando Torres in attack and he was thwarted by Tremmel with the goal gaping after twice being set up by the returning Juan Mata.
"Today I can say the biggest responsibility for the lack of goals was the Swansea goalkeeper because he made three or four big saves," said Mourinho.
"He played really well and also this time I complain about a big penalty decision so my words have changed a bit," he added, referring to a foul on Belgium winger Hazard.
"We didn't miss chances, Tremmel made fantastic saves. The first-half save from Eto'o was brilliant and the first save in the first minute of the second half from him was the same.
"That action was good. David Luiz's pass was good, Mata's control and pass were fantastic and Eto'o attacked the ball perfectly."
Brazil midfielder Ramires picked up his fifth yellow card of the season and will be suspended for Chelsea's home game against fourth-placed Liverpool on Sunday.
(Editing by Ed Osmond)
