City are now clear favourites to win the top flight after moving back to the summit with their 2-0 victory at Old Trafford on Wednesday.
The champions, who have won their past 11 league games, are a point ahead of Liverpool with three matches remaining for both clubs.
The derby was seen as the toughest hurdle left for City as they bid to become the first side to retain the title in a decade.
"If you have this late a derby and you win this big game, it gives you a lot of confidence, especially when you have just three games left to play," said Sane, who came off the bench to score City's second goal. "Every one of us wants to do the back to back. We're really happy about this win because it is the derby, a special game, and also really important for the Premier League."
Sane recognises the job is far from done, however. With such a slender lead City can ill afford any slip-ups in their remaining fixtures, starting with Sunday's trip to Burnley.
The German winger said: "Like we did all season (we must) stay focused. Now we just have to rest and then focus again for Burnley. The last three games won't be easy at all."
Pep Guardiola's men had to bide their time at Old Trafford but their superiority showed as United tired in the second half.
Bernardo Silva made the breakthrough in the 54th minute and Sane doubled the lead following a quick counter-attack 12 minutes later.
City then comfortably saw out the game, the only downside being an injury to Fernandinho. The Brazilian was withdrawn as a precaution after hurting his knee blocking a shot from Paul Pogba.
He will have a scan and be assessed ahead of the next game at Turf Moor.
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