City kept their fate in their own hands on Wednesday, beating their city rivals 2-0 to leapfrog Liverpool back to the top of the table with a one-point advantage.
It took some time for the defending Premier League champions to get going before Bernardo Silva lashed a shot past David de Gea in the second half to secure a lead that would never truly be threatened.
Leroy Sane's shot that was diverted in by De Gea sealed the points, leaving City three games away from another league title while keeping the hopes of a historic domestic treble alive.
But Kompany says the job is nowhere near complete.
"We didn’t start as well as we’d have liked it but that can happen," Kompany told Sky Sports.
"We defended well when we needed to and in the second half we got into our rhythm. In the second half we were there to score goals.
"It’s significant because it’s a derby. In the league, nothing is played out yet. Burnley is a difficult away game next and there is plenty to play for both for us and Liverpool. We will deal with the other games in the next days.
"We need three wins. We cannot expect the opponent to drop points. We'll get back into our routine and if everyone does the right thing and this team prepares well we always have a big chance to produce a good performance."
Having already secured the Carabao Cup, City's treble hopes are alive, and Sane says the focus turns towards those remaining matches and the tall task of holding off Liverpool.
"It was a difficult game. The first half we had problems but in the end we did it well. We were patient and played our game," he told Sky Sports.
"Pep Guardiola always tries to help us to see what we did not so good, as well as what we did good, showing us examples [at half-time].
"In every game if you sit on the bench you hope to come on. Especially in the derby. I was waiting and hoping.
"When Raheem [Sterling] passed the ball I knew I had to react quickly.
"We just try to enjoy and work hard and focus on us. It’s in our hands."