Despite having a numerical disadvantage following Chris Smalling's red card, United finished the game strongly and carved out a couple of opportunities to equalise.
However, regardless of the fact that they ended the match on the back foot, Kompany has insisted that the 1-0 win is all that mattered as City secured local bragging rights.
"The league doesn't matter for a minute, the Champions League doesn't matter. Winning the derby is massive and it gives us our city back," he told Sky Sports News.
Next up for City is a Champions League group encounter against CSKA Moscow on Wednesday night.