Roberto Mancini's team were frustrated when they lost a two-goal lead to draw at Fulham last weekend after being held 1-1 in their Champions League opener against Napoli.
But despite facing a stubborn and well-organised Everton side, they found a way through at Eastlands, with Mario Balotelli and James Milner coming off the bench to score the goals.
They have now won five of their six Premier League matches this season and Kompany thinks that Mancini's expensively-assembled team is starting to gel.
"We showed a lot of positive things and we're really happy with the performance," he said.
"Maybe on any other day we might have got frustrated but they did exactly what Napoli did and it wasn't' a surprise.
"With the quality we have sometimes it's just a matter of patience and the goal will come. Maybe we didn't impress but we did what we needed to do and it's another step forward."
Mancini was pleased with the performance of Balotelli and insists the Italian has reacted well to being on the fringes of his squad this season.
The Italian, who is suspended for Tuesday's trip to Bayern Munich, has struggled to stay out of the headlines since joining from Inter Milan in the summer of 2010 and has drawn criticism for his failure to even smile when he scores.
But he swung Saturday's game in City's favour, sweeping in a fine finish before running to hug his manager.
Mancini thinks he can play a key part this season if he continues to show such a work ethic.
The manager said: "Mario didn't play for three or four games but he worked well and didn't say anything and waited for this moment. I enjoyed it for him, he scored an important goal.
"Now it's important that he continues to improve. Mario is a good guy. Some of his behaviour is so-so but he's a good guy. He likes Manchester City and English football and he was really happy.
"Sometimes when he scores he's unhappy but he knew that was an important goal."
Everton manager David Moyes is hopeful that Tim Cahill will recover from injury to feature in next weekend's Merseyside derby against Liverpool.
The Australian midfielder went off with a shin problem after a challenge with Kompany.
"It looks like it's just a bruised shin but it was a terrible tackle and his foot went right on his shin. I've seen it again and it's disappointing that it wasn't spotted," Moyes said.
For all his frustration, Moyes admits that City will mount a strong challenge the Premier League title this season.
He feels that David Silva is City's key man and employed Jack Rodwell to shadow the Spaniard throughout Saturday's game.
"We did a job on David Silva and did it well, He's a big part of what they do, the biggest part, and we did a good job on him," Moyes added.
"They've got a really talented team, an excellent team. They will be contenders, no doubt."
Source: AFP
Source: AFP