The 3-1 aggregate scoreline sees the Blues through to the quarter-finals of the Champions League, thanks to goals from Samuel Eto'o and Gary Cahill.
Mourinho spoke at a press conference of his delight at the result, noting no comfort at half-time, per Chelsea's Twitter account:
Mourinho: 'A very good performance. Very solid. Very compact. No fears.' #CFC— Chelsea FC (@chelseafc) March 18, 2014
Mourinho: 'The team were very confident and in control for the full 90 minutes, which is difficult.' #CFC— Chelsea FC (@chelseafc) March 18, 2014
Mourinho: 'We got a positive result in the first leg, and in the second leg we finished the job.' #CFC— Chelsea FC (@chelseafc) March 18, 2014
Mourinho: 'The result at 2-0 is still difficult at half-time.The 2-0 kept the result alive until the end, but we were in control' #CFC— Chelsea FC (@chelseafc) March 18, 2014
Mourinho on the next round: 'All the big candidates are still there. It's good for the evolution of the team to play a big team.' #CFC— Chelsea FC (@chelseafc) March 18, 2014
There was plenty of talk before kick-off of just how Didier Drogba would move to influence the match at Stamford Bridge.
However, it wasn't the night for Drogba to mark his Bridge return with a goal, and Mourinho spoke of how his defence kept him at bay:
Mourinho on Drogba: 'It was difficult for him because of how his team played. He couldn't do much.' #CFC— Chelsea FC (@chelseafc) March 18, 2014
Mourinho on Drogba: 'I will say that Cahill and Terry were fantastic though, against very good strikers.' #CFC— Chelsea FC (@chelseafc) March 18, 2014
Galatasaray boss Roberto Mancini also noted similar views to Mourinho in his press briefing, believing that his side were below par in London, as tweeted by per beIN Sports' Tancredi Palmeri:
Mancini: "Tonight we have been our shadows, we played badly. I didn't expect such a failure"— Tancredi Palmeri (@tancredipalmeri) March 18, 2014
However, it was strike counterpart Eto'o that showed the early sight for goal, putting Chelsea into the lead after just four minutes.
From a throw-in, Eden Hazard broke free of Emmanuel Eboue to collect the ball, with an exquisite pass from Oscar feeding the ball into Eto'o.
From inside the box, Eto'o showed calmness in front of goal to squeeze the ball under outstretched goalkeeper Fernando Muslera.
ESPN FC tweeted of how the Cameroon forward's goal had put him level with fellow his African competitor:
Only two Africans have scored 30 Champions League goals. Both are on the pitch at Stamford Bridge (Eto'o, Drogba).— ESPN FC (@ESPNFC) March 18, 2014
Cahill then made it 2-0 to Chelsea just before half-time.
The corner, whipped in by Frank Lampard, was first met by the head of John Terry, which pulled a save from Muslera that the stopper could only palm back into danger.
The ball then dropped nicely to Cahill just a few yards out to smash home the Blues' second with minutes to go until the interval.
It was during this half-time break that Mourinho didn't feel comfortable at the Bridge, realising the potential damage that Drogba could cause.
At 2-0, Galatasaray needed just two goals and for Chelsea not to score to see the Turkish side through to the next round.
Lampard could have made it three with a bullet header on 63 minutes, but his effort was placed straight into the arms of Muslera.
Hazard also had an excellent chance to see the game out on 83 minutes, as his right-footed curling effort had to be forced away by the goalkeeper.
Galatasaray tried but could not muster the final ball to bring their game back to life after plenty of chances.
Didier Drogba twice had an excellent chance to put the side ahead, but two fierce shots were rifled into the upper echelons of the Bridge's loyal supporters.
The result sees Chelsea through to the quarter-finals as Mourinho looks to mark his first year back at the club with their second Champions League title.
The draw for the quarter-final stage will be made on March 21, according to UEFA.com.