The Egypt international was snapped up by the Blues in January, as they pipped Premier League rivals Liverpool to his signature.
Salah has arrived in England from Swiss outfit Basel, with Chelsea having been impressed by the contribution he made during the UEFA Champions League fixtures against them in the group stage of this season's competition - as he netted twice in two shock defeats for the Blues.
He has been acquired with one eye on the future, with it difficult for any 21-year-old to make an immediate impact in new surroundings.
Mourinho is prepared to give the youngster time, with his early outings for Chelsea having all come from off the bench.
The Portuguese coach said of his £11million winter window recruit: "He was not in the game (against Manchester City). He has that (pace) but he was not in the game.
"It's important for him to come step by step and try to improve and adapt. This is a different world, a different quality of football to the one he comes from.
"You know, playing at Stamford Bridge is not the same as playing for Basel.
"With Basel you play to enjoy your time and you have nothing to lose. While in the blue shirt, you have 40,000 people that you are required to please. Everyone wants you to be decisive, all the time.
"So I think Mohamed needs six months to adapt to our game and the demands of the Premier League.
"I am calm and I'm telling him he has time because we have confidence in him. I think next season is Mohamed Salah's breakthrough season."