Raheem Sterling spoke of his delight after his first hat-trick in English football, while Manuel Pellegrini stressed the need to keep on working on his finishing.
The £49million summer signing has been criticised for his lack of potency in front of goal but he rose to the challenge in the absence of Sergio Aguero with a superb display against the promoted Cherries.
Wilfried Bony also struck twice as the Premier League leaders eased to a comfortable victory at the Etihad Stadium.
Sterling, who also scored for England during the recent international break, said: “It’s my first hat-trick and I’m delighted.
“I definitely work on my finishing. I get a quite lot of chances and it’s something I’ll keep working on and hopefully get better at.
“Most importantly though, I’m happy that the team got the three points. I think we played some good stuff at times and I’m really happy with the three points.”
Manager Manuel Pellegrini also backed the 20-year-old, whose goal tally for the club now stands at five, to continue improving.
Pellegrini said: “I think it was important for Raheem to score three goals. He must improve his finishing – he did that today. He’s young and will continue to get better.
“I don’t think he’s a striker like Kun (Aguero) or Bony but this year, and I said it when he arrived, I am sure he will score more goals than he did in another season at Liverpool.
“Kevin (de Bruyne) did very well, as he did against Newcastle, and I think the system allowed Raheem to score more goals.”
Sterling’s performance contrasted with his last appearance for City, when he was substituted at half-time in the 6-1 win over Newcastle after an ineffective display.
Pellegrini said: “He didn’t lose confidence because I spoke with him immediately after he came off. He didn’t play well but all of the players can have a bad day.”
The one notable selection issue was Pellegrini’s decision to put captain Vincent Kompany on the bench. The defender had missed City’s five previous games with a calf injury but then played for Belgium in midweek, much to Pellegrini’s displeasure.
Pellegrini said: “He was on the bench because we finished playing with (Nicolas) Otamendi and (Eliaquim) Mangala in the last game and they did very well.
“He was on the bench because he played for Belgium on Tuesday and couldn’t work on Wednesday and Thursday. I think working just one day after one month injured is not enough to play again.”
Midfielder Yaya Toure was withdrawn at half-time but this was more about easing the Ivorian back into action after a hamstring injury than thinking about this week’s Champions League challenge.
Pellegrini said: “It was not thinking about Sevilla, it was thinking about Yaya. In the first 10 days of the international break he did nothing so I thought 45 minutes was enough.”