City moved back to within six points of league leaders Liverpool with the victory, while their game in hand and superior goal difference mean that they are in prime position to pounce upon any slip-ups from the Reds in the final games of the season.
Kompany believes that his side can take inspiration from their 2011-12 title success, when Sergio Aguero scored deep into injury time on the final day of the season to snatch the crown from neighbours Manchester United.
"It's job done and we had some good spells in the game. We'll take it with us in the final four games. We can still remember what happened for us two years ago," Kompany told Sky Sports News.
"We take motivation out of it but the most important thing is that we get back to the form we had at the beginning of the season. It looked like we were better against West Brom and if we take that into the next four games anything can happen."
"We knew David was struggling. He's been great for us and he put in a shift. Hopefully he'll be back soon," he added.
City face Crystal Palace in their next match on Sunday before ending the campaign with games against Everton, Aston Villa and West Ham United.