Samuel Eto'o opened the scoring for the hosts after just four minutes on Tuesday night when he fired past Fernando Muslera before Gary Cahill slammed home a second from close-range moments before the break.
Didier Drogba's Stamford Bridge return had dominated the headlines in the build-up to the game, but the striker rarely caused a threat and his side gave the Blues little to think about as they eased to a 3-1 aggregate win.
Mourinho said: "It was a very good performance, very solid, very compact, no fears and a very good approach to the game.
"Even if you are winning 2-0, it is difficult because if they score one goal you are on the limit. The team was very solid and confident and very much in control for the 90 minutes which is difficult to do.
"The 2-0 score kept the game alive to the end but the way we played was very solid so even with 2-0, we were very much in control and had the best chances to score again.
"Probably the result could have been much bigger because we were much better than Galatasaray."
Drogba had a subdued Stamford Bridge return but Mourinho believes that this was down to a lack of service and the close marking of his defenders.
"The most difficult thing was the way his team played. For every striker in the world, if your team doesn't produce attacking football then you feel a lonely man," he said.
"So he couldn't do much and Gary Cahill and John Terry did a fantastic performance against two very good strikers. We controlled the game so well that we didn't see Drogba in dangerous positions."
Mourinho also says that Manchester United can still win the competition if they overcome their 2-0 deficit against Olympiakos and join his side in the last eight.
"I keep saying the same, I believe that while Man United are in the competition they can do it, and I hope they do it tomorrow," he said.
"All the big candidates to win the competition are there in the draw and I welcome anyone of them. It will be good for our evolution as a team to play the best and we wait for the draw, it doesn't matter who."