The win – just Chelsea's fourth in 13 league games this season – ended a run of three successive Premier League defeats for the champions.
Chelsea had Diego Costa to thank for the only goal of the game although the Spanish international had been guilty of wasting two decent chances to score in the first half before slotting past John Ruddy just after the hour.
Mourinho admitted it would have been hard for Costa to handle had his side failed to win the game.
"Diego missed two big chances in the first half and if he did not score it would be a big 50 kilo on his back, but he scored and he could breathe easy," said the Chelsea boss.
Chelsea, 2/5 to win away to Maccabi Tel-Aviv in midweek, were the better side for much of the game but found it hard to break down a resolute Canaries side. Mourinho said his side were worthy winners although he felt they could made things less problematic.
"The only thing we didn't do was score more from the chances we had. We should have scored at least two and breathed easier, but it is difficult for us to score goals and to keep a clean sheet against a team who plays defensively and then has a try in the final few minutes because they had nothing to lose," he added.