Remy scored Chelsea's third in Wednesday night's 3-0 defeat of Tottenham after Drogba, starting in place of the suspended Costa, had made one and scored another in the Barclays Premier League leaders' comfortable win.
The France striker, who has recovered from a niggling groin problem, told Chelsea TV: "I felt very happy after this goal
When you're a striker you want to score every game.
"The opportunity was there because Diego wasn't involved
Didier played well again.
"For me it's important
I took my chance and scored this goal
I can give him (Mourinho) another opportunity and he can count on me any time he wants."
Chelsea, who failed to score for the first time this season at Sunderland last Saturday, began on the defensive as Spurs chased a first win at Stamford Bridge in almost 25 years, before Mourinho's men stepped up.
"We know that we can score any time," Remy added.
"The squad is really strong and that makes the difference between us and the other teams.
"We will keep going to try and keep the distance from our closest opponent
It's six points and that's really good
We try to continue in this way."
Eden Hazard opened the scoring after a one-two with Drogba, exploiting Aaron Lennon's failure to track back.
Hazard, who struck his fifth Premier League goal of the season, told Chelsea TV: "I try every game to score
If it's not a penalty, another goal.
"The fans want me to score, the players want me to score
I scored a good goal and helped the team to win the game.
"We were in control
We created a lot of chances
We gave nothing away
Our team was very good."
It was a fourth successive clean sheet for Chelsea ahead of Saturday's trip to Newcastle, with Hazard praising the collective contribution.
"Defensively we are very strong," he said.
"All the players want to defend for the team, even the attacking players, even me
We are very strong and it's important.
"It was important to win because we lost two points last week against Sunderland.
"We scored three beautiful goals
We are six points in front and we want to stay there."
Harry Kane might have put Tottenham in front, but hit the bar with a header before firing wide across goal.
The striker, who was not even born when Spurs last won at Stamford Bridge in February 1990, insists his side cannot dwell on the result, with another derby coming up this weekend, against Crystal Palace.
"We started very well, we created a few chances and hit the bar with a header," Kane said in the London Evening Standard.
"On another day it could have dropped in
We created a couple of others, too
They didn't go in, either, and Chelsea punished us for it.
"They're a good side and it's something we have to learn from
They were just more ruthless than us.
"But we have to dust ourselves down because we have a big game coming up at the weekend.
"We can't dwell on it too much
There are too many important games coming up that we have to win, starting this weekend
We have to keep up the intensity in games and do well.
"Everton (a 2-1 win last Sunday) was the benchmark of how we have to play this season and hopefully we can go beyond that and keep improving."
Source : PA
Source: PA