Pep Guardiola claimed his Manchester City team would need to improve after labouring to a 3-0 victory at Premier League bottom side Huddersfield.

The champions were far from their best but still proved too strong for the managerless Terriers at the John Smith's Stadium on Sunday, winning with goals from Danilo, Raheem Sterling and Leroy Sane.

Victory cut Liverpool's lead at the top of the table to four points and City have now scored 102 goals in all competitions this season, but Guardiola still expects more.

He said: "Today we are happy we have won but immediately we have to analyse what we have done and to win in the future we have to play good.

"During the season you have games when maybe you are not in the top level and it is important to win these games.

"All the teams have that but to arrive in the last stage of competitions our game will have to improve."

Asked how he could expect his side to get better, Guardiola said in his post-match press conference: "Our pace, more passes in a row – we were not able to make a lot of passes. Always in football when you play good you have the ball as much as possible."

Danilo's heavily deflected strike gave City an 18th-minute lead but it was not until Sterling and Sane struck in quick succession early in the second half that the points were made safe.

Sane revealed Guardiola had demanded an increase in intensity during the interval.

The German winger said: "The second half everyone could definitely see we were quicker and better and in important positions and controlled the game. It is easier when you can play like that and you can push forward more.

"The boss said at half-time that we can't play the way we were playing and that we had to get better.

"They were putting us under some pressure too and we know in the Premier League that a goal can come out of nowhere and at 1-1 it would be difficult to get the win.

"So he woke us up a bit to play our game quicker and better and help us find where the space is."

The game was Huddersfield's first since the departure of their popular manager David Wagner last Monday.

The defeat was their ninth in 10 games – the other being a draw – and left them 10 points off safety but caretaker manager Mark Hudson was pleased with the players' efforts.

Hudson said: "It has been a long week, I enjoyed it, especially as the players took on board what I asked and they fought until the last seconds of the game. I said thank you to all the players for what they have given me."

Borussia Dortmund coach Jan Siewert has been linked with the vacancy but Hudson does not know if an appointment is imminent.

Siewert was not at the game, even though a TV reporter mistook someone in the directors' box for the German.

Hudson said: "I was asked to take charge this week, leading to Sunday. For this week I will have a few conversations later today or tomorrow and see where we go."