The Egyptian opened the scoring in a 3-0 win against Stoke City at Stamford Bridge on Saturday before goals from Frank Lampard and Willian secured the three points that sent Chelsea back to the top of the Premier League.
Salah, whose signing from Basel coincided with Juan Mata's departure for Manchester United, is just 21 and Mourinho believes that Chelsea have secured a promising talent.
"I think Chelsea did very well. We sold a player [Juan Mata]...in the best moment of his career and we bought a kid from a different habitat, an Egyptian player playing in Switzerland," Chelsea boss Mourinho said.
"We knew that the kid was going to need time. We know that the next season he will be a real good player for us.
"This season step by step, he starts playing, 10 minutes here, 10 minutes there, he came on against Newcastle, he came on against Arsenal, against Crystal Palace.
"Today he had the first chance to play [from the start] and I think one thing you feel immediately is the connection between him and the crowd; they like him, they like his style of play and he is player that we need.
"We have wingers who like to have the ball at their feet he is the kind of winger who prefers it in the space.
"Chelsea did very, very well to bring him in."
The result helped to ease the pain of back-to-back losses for Chelsea, who were beaten 1-0 at Crystal Palace in the Premier League before suffering a 3-1 defeat to Paris Saint-Germain in the first leg of their Champions League last-eight tie.