g of Maribor
Remy, starting again due to top-scorer Costa's ongoing hamstring problem, scored the opening goal before departing after 16 minutes to be replaced by Didier Drogba, who scored the first goal of his second spell at Stamford Bridge from the penalty spot.
Remy has a "muscular injury" and faces a period out, confirmed Mourinho, who does not expect Costa to be fit for Old Trafford.
The Blues boss added: "I don't know the dimension and I'm not worried
When a player is injured, play another one.
"Tomorrow is a day off and the doctor is forbidden to call me to speak about injuries
I don't want to speak about injuries, Man United
I don't want to know.
"We don't cry on injuries
It's our philosophy, we don't cry
We just think one injury means an opportunity for somebody else.
"We cannot hide
In this moment we have some problems with players that are not available to play.
"We will prepare the game Thursday, Friday, Saturday to try to be at our best possible level against an opponent which we respect very, very much."
Drogba, whose final kick of his first spell was the last penalty in the shootout defeat of Bayern Munich which saw Chelsea win the 2012 European Cup, is 36 years old and has only just returned from an ankle injury.
Mourinho on Monday insisted Drogba was not ready to play 90 minutes, but was happy with the Ivory Coast striker's performance as he scored his 158th Chelsea goal.
"I was not expecting him to play 75 (minutes)," Mourinho added.
"I spoke with him yesterday and we spoke about 30
He had to go on.
"He was comfortable to play 75 minutes
It was very, very important for Didier
The best thing for a player to improve his condition is to play.
"His last goal for Chelsea was the most important goal in the history of the club
So to be back and to score again at Stamford Bridge is nice for him
Eden Hazard is the regular penalty taker and Mourinho was not totally content that Drogba persuaded the Belgian to give up spot-kick duties.
"I don't like," Mourinho added.
"They have the freedom to do it
They can do it, but he has to score."
Remy and Drogba's goals were followed by captain John Terry's strike - following a length of the field run - an own goal, a Hazard penalty and the Belgian's last-minute sixth.
"The best way to respect opponents that, in theory, are not so good as you are, in my opinion, is to play the maximum you can," Mourinho added.
"(At) 3-0 at half-time, many, many, many occasions you stop, you just control
They kept enjoying the game and playing and trying to score
Being happy on the pitch."
Despite the resounding win which leaves many suggesting the Blues are among the Champions League favourites, Mourinho refused to look beyond the group phase
"We have played three matches," he said.
"To be in the final you have to play 12 and qualify for the final
Long way to go.
"I think it's premature to speak about that
We are not even qualified for the next phase.
"Step by step
First objective is to qualify, second objective is to finish first in the group."
Maribor boss Ante Simundza conceded Chelsea were at another level.
He said: "It was obvious that this was a team that is a serious candidate to win the title in this year's Champions League.
"Quality of the players was out of reach for us
Chelsea were just the better team and deserved to win all three points.
"We conceded three goals from counter attacks and we might have been a little bit naÃƒÂ¯ve.
"Regardless of Chelsea being a good team, they had an exceptional day today."
The sides meet in Slovenia on November 5.
Simundza added: "The home match will be tough like this one, because Chelsea have a really good team.
"Maybe in the home game we'll have more chances and start to believe
I know we can be better as a team."
Source : PA