Fulham proved obliging opponents for a team entering a defining week in their Premier League season, little more than a means for Manchester City to improve the goal difference that Yaya Touré believes could be crucial come the finale. But ideal preparation? Not quite. Intensity and aggression were unnecessary as City sauntered to victory and left Felix Magath fuming at his team's "lack of fight". A bruised Manchester United and a battered Arsenal may not be so accommodating.

"Both games are important because we have to be sharp, clever and strong," said Touré who, with the superb James Milner, led the dissection of the league's bottom club. "United are not doing so well but you have to be careful against them and Arsenal, after losing to Chelsea, will be hungrier and want their fans to believe again.

"People have been describing United as being not so good at the moment, but we have to be careful because derbies are never the same and they will have a lot of desire to try to beat us. We have to do the job, play together and be strong – and any chance we get to score we will have to take it. This year will be very tight so it's important that we scored a lot of goals against Fulham. Now I hope [Sergio] Agüero can come back very soon because he is an important player and we need him."

Agüero is expected to miss Tuesday's trip to Old Trafford with a hamstring injury but return at the Emirates on Saturday. In the absence of the Argentina international and the ill Edin Dzeko, and with Álvaro Negredo visibly low on confidence after no goals in nine outings, Touré took responsibility to rout Fulham with his first hat-trick in English football.

The treble arrived from two penalties conceded by the error-prone Fernando Amorebieta, a soft kick up Negredo's backside and a clear trip on David Silva leading to his dismissal early in the second half, plus a stunning shot curled just inside David Stockdale's left-hand post from 25 yards. The Ivory Coast international now has 20 goals for the season from midfield and a convincing response to criticism that his defensive duties are occasionally abandoned.

Touré said: "It was my first hat-trick because I have always been involved on the defensive side. Now I am very happy because the manager has given me the confidence and more freedom to go forward. Sometimes when we play four in attack it can be very difficult because we leave space and there are teams who play very well on the counterattack. We managed that very well against Fulham, and [Martín] Demichelis and [Joleon] Lescott did a brilliant job, as did [Pablo] Zabaleta and Fernandinho. Keeping a clean sheet was also important to be ready for the games coming up."

Fernandinho and Martín Demichelis completed the scoring on an afternoon when most of City's brightest, more incisive moments involved the tireless Milner. The spread of goals and chances – Milner, Aleksandar Kolarov, Silva and Negredo could have added their names to the scoresheet – reflected a well-balanced, potent side in the eyes of Manuel Pellegrini.

The City manager said: "The way Yaya plays he can score, but maybe if I asked Yaya to stay a bit further back and defend more he wouldn't score as many goals. I think we have a great balance with our midfielders – Fernandinho also scored – and it's important for both of them to defend and attack. I think with those kind of midfielders, who are so good technically, we can do damage to any team.

"There are not many players like Yaya, which is why it's very important to know how to defend with these players. It's not easy. Maybe at the beginning of the season we didn't do it so well but at the moment I think we are the second-best defenders in the league. It's important to have good players but also how to defend as a team."

By contrast, Magath was damning in his assessment of a Fulham display that began resolutely and with purpose, yet ended the moment the referee, Jonathan Moss, penalised Amorebieta for the first spot-kick. "It was too easy for them in the end," said the Fulham manager. "The last 30 minutes were poor because we lacked fight. We still had 10 players on the field and I wasn't happy with the last 30 minutes. We had started well but we stopped playing. There was a lack of fight. We were in a good moment, but then the penalty is given and we didn't have enough confidence to deal with the situation."

Man of the match Yaya Touré (Manchester City)