Eden Hazard's first-half strike was enough to ensure the Blues collected three points ahead of Sunday's crunch clash against fellow title contenders Liverpool.
Mourinho's men created enough chances to have put the Swans to the sword by half-time, with striker Samuel Eto'o enduring a particularly frustrating day in front of goal.
"They kill me," Mourinho told reporters. "Every game I am tired.
"At half-time we should be relaxed with a comfortable result and we were not. The first thing that happens in the second half was the biggest chance of the game and after that we had a clear penalty [not given].
"If you read all these things you think we would go home with a comfortable result but the time goes on and you don't score, and the opposition starts to believe.
"But the boys worked hard defensively in that part of the game, and the biggest responsibility for the lack of goals was the goalkeeper, who made three or four tremendous saves."
The Portuguese refused to criticise the performances of forwards Eto'o, Fernando Torres and Demba Ba, however, despite their failure to match the goalscoring totals of some of the leading lights of their Premier League rivals.
"They always give something to the team," he added. "No winning goals, but they give what they can."
Mourinho praised man of the match Hazard's willingness to dig in as Swansea searched for an equaliser in the latter stages of the game having shone as an attacking force for most of the contest.
"He gave everything and his last action in the game was defending against their left-back in our box in a situation of danger," he enthused. "When I took him off he was exhausted."
Swansea boss Michael Laudrup, however, argued that it was unrealistic to expect Chelsea not to have periods of dominance on home turf.
"In terms of chances I think it is more or less what I expected," he reflected. "You will not create lots in these games. When you play teams like this they have quality players that will make the difference.
"I thought the intention from Chelsea (after the goal) would be to try to finish the game off.
"But i think we came okay in the game again and the fact that we were in there until the last second was positive."