Pep Guardiola says his team must improve if they are to overhaul Liverpool at the top of the Premier League and fulfil the sky-high ambitions they have for this season.

Goals from Danilo, Raheem Sterling and Leroy Sané gave Manchester City a comfortable win at bottom-of-the-table Huddersfield and cut the distance to the leaders at the top of the Premier League back to four points. But Guardiola, whose team are pursuing trophies on four fronts, said better performances will be needed as the season approaches its climax.

“If we want to achieve something and arrive in the last stages of all competitions, our game has to improve,” said the Catalan, whose side seemed uncharacteristically lethargic and sloppy at Huddersfield, especially in the first half. “More pace, more passes in a row,” said Guardiola when asked how his team must improve. “We were not able to make a lot of passes, 10-15 passes in a row. When a team defends like [Huddersfield], you have to commit sometimes to move them a little bit. That is what we have to improve. Always in football when you play good you have the ball as much as possible. Here we had the ball but not in effective positions and sometimes we lost the ball quite easily.”

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If that was a wake-up call to his players as they chase Liverpool and prepare for a Champions League showdown with Schalke and an FA Cup fourth-round tie against Burnley and, surely, a Carabao Cup final, it would be a stretch to say Guardiola is alarmed. “During the season you have these kind of games, you cannot always be at your best level,” he said of the performance. “We are happy we won but you always have to analyse what you have done. Hopefully we can improve in the next games.”

Mark Hudson, meanwhile, said he was satisfied with his team’s spirited performance against City and said he enjoyed being in temporary charge of Huddersfield following Monday’s departure of David Wagner. Hudson is set to revert to running the club’s Under-23 team after the Yorkshire club entrust their senior team to a new full-time manager, with the head of Borussia Dortmund’s reserves, Jan Siewert, set to be announced this week.