Pep Guardiola challenged his Manchester City stars to keep firing on all cylinders as they look to maintain their position on top of the Premier League.

Guardiola's side moved ahead of Manchester United on goal difference with a 5-0 demolition of lowly Crystal Palace at Eastlands on Saturday.

City have now scored 16 times in their last three top-flight games, but Guardiola is demanding more from his players after they struggled to turn their dominance into goals in the first half.

"Nobody went to take the ball and start to play, so it's five or 10 seconds before someone moves and takes the ball," he said.

"When that happens, everything is slow. The ball boys were slow, everybody was slow.

"We have to be creative and provoke the situations and we didn't for most of the time in the first half."

City's performance after the break pleased Guardiola more and was closer to what he's demanding of his team for the visit of Shakhtar Donetsk in the Champions League on Tuesday.

"I know Shakhtar very well from my period in Barcelona and Bayern Munich, we played a lot of times," he said.

"They were able to beat one of the best teams in the world right now, playing football against Napoli.

"We cannot get distracted because in the Champions League group we need to be careful."

Guardiola is calling on City fans to turn out in force for that fixture despite their frosty relationship with the competition and UEFA.

"We need our fans, hopefully they can come. I know they have more problems in the Champions League," said Guardiola.

"In the Champions League, you are in real trouble if you have one step back.

"If we can win, we'll take a huge step to be in the knockout round in February.

"Hopefully we can learn from what we didn't do well (against Crystal Palace) and play, win the game, and go with confidence to our game in Chelsea."

- Headache -

Meanwhile, Crystal Palace boss Roy Hodgson is bracing himself for a tough few weeks.

With games against Manchester United and Chelsea on the horizon, the former England manager is aware his team could be in deep trouble, as they're still yet to earn a point or score a goal in the Premier League this season.

"We've got to accept that we've been given a headache and during the course of the week we've got to try and find the aspirins that will ease the headache," he said.

"We've got to keep working on the things we've been working on because, unfortunately, there's a risk that Man United and Chelsea would also be as capable as Man City have been of punishing us if we don't get things right."

Hodgson has previously saved Fulham when they looked doomed to relegation in 2008, taking nine points from his final three games.

"It's an equal challenge without a shadow of a doubt, but the difference is when I came in to Fulham there were 18 games to play," he added.

"Here we've still got 32 games to play, so a lot of things can change.

"It's unlucky after a bad start of no points from five games that you run up against teams of this quality, so it's a baptism of fire.

"We have to make certain that we don't start panicking and start accepting that we're in a hopeless position at the end of September because the remaining months can change so many things."

Mourinho cautious despite fast Man Utd start

Manchester United manager Jose Mourinho says it is too early to talk about a challenge for the Premier League title despite watching his side win their fifth match out of six.

United, who have not won the title since Alex Ferguson was at the helm in 2013, are second in the table, level with Manchester City on 16 points, but with an inferior goal difference.

The Portuguese manager conceded his team have started better than last season but sees next month, when they face Liverpool and Tottenham Hotspur, as more significant.

"I know that last season (by) this fixture I think we would have, maybe, five or six points less than we have this season," he said. "So we are better this season than last.

"But this is nothing. It's just a start. A difficult period with an accumulation of matches, that comes in October. I really think that six teams are going to fight for the title."

Manchester City's 5-0 demolition of Crystal Palace on Saturday took them clear of United at the top but the hard-fought 1-0 win at Southampton showed off United's battling qualities instead of the attacking prowess they have demonstrated in recent weeks.

But United's victory was marred by more crude chanting from the away fans about goalscorer Romelu Lukaku.

United looked likely to win comfortably after Lukaku's 19th-minute goal, but had to rely on a hard-pressed defence in the second half and Mourinho praised Phil Jones and Eric Bailly's performance in the centre of the defence.

"And also Chris Smalling," he said. "We did for the last 20 minutes what the majority of the Premier League teams are doing, which is to play defensively with five at the back. We had chances to kill the game and score the second goal, but didn't."

- Fatigue -

The United boss, who was sent to the stands late in the match, said warm weather on the south coast had taken its toll on his players.

"The last time we had this was in Los Angeles and then in Macedonia, and I think they felt (it). I saw some players not sharp. Great spirit and always trying, but not the same sharpness. So if your opponent is coming with everything against you, let's do it for 10 or 15 minutes and stay solid."

He said he was baffled by his red card, which appeared to follow a collision with the fourth official and suggestions that he encroached on the field of play as Southampton pressed late on. "I don't know," he said. "Craig (Pawson, the referee) told me to leave, and I left."

Southampton boss Mauricio Pellegrino was pleased by his team's performance despite a ninth blank at St Mary's in 10 home games.

"To play with this spirit and with this football we will win more games than we lose and we have to continue in this way. They (United) realised that we were playing well and they defended. That is football too and you cannot always play really, really well. The best teams adapt to their situations."

United reiterated their condemnation of the crude chant about Lukaku after it was aired again during Saturday's match.

Both United and Belgian striker Lukaku had previously implored supporters to stop singing the song, which draws on racial stereotypes about the size of black men's penises.

But fans sang it again at St Mary's, as well as "We're Man United, we'll sing what we want", and the club now plan to use CCTV footage to identity the offenders.