Lampard said: "I think we are a few points short of where we should be, based on our performances and that is not bad luck, just me being self-critical because there are games where we should have gained more points from so that is on us, but I'm pretty happy.

"I am happy we are in and around the (top) group. Obviously Liverpool are out on their own at the minute, but at this early stage we are in a nice position.

"This should give us determination to go away (for international duty) and come back in the same vein because the minute you relax in this league it can all change very quickly.

"The reason we are playing well is because of how hard we are working and how together we are. If we can keep that going, then we will be challenging right up there I hope."

Abraham opened the scoring on the south coast with an excellent lob over Angus Gunn after racing on to Callum Hudson-Odoi's fine through ball in the 17th minute.

Portsmouth-born Mount doubled their advantage seven minutes later, curling home before cupping his ears to the Southampton supporters.

But Danny Ings pulled one back, after Yan Valery dribbled beyond Fikayo Tomori, and Lampard focused on the areas where Chelsea can improve.

"A lot of weeks I will say the boys at the back have been brilliant and they have recently, but we can't afford to give little moments," he said.

"That is a pointer for all of us that we are not there, we are nowhere near the finished article. The benchmark is Liverpool and City and how they play, so we need to cut out those little bits."

Kante's deflected effort put the Londoners 3-1 ahead at half-time and substitute Batshuayi drilled through Gunn's legs with a minute left – after Christian Pulisic's excellent through ball – to conclude the scoring.

A negative for Chelsea was the away fans chanting a song about Lampard which referred to West Ham as 'pikeys' and he addressed the issue.

"It does go on. I watched a game on TV (on Saturday) where I heard similar stuff from other clubs and none of us want it. I have said it before here," the Blues manager said.

"I will always back the Chelsea fans in how they support us, but with that we don't want them to chant stuff which is discriminatory to anybody and anyone. We all need to look at it. It is a wider problem than just Chelsea, but it shouldn't stop us talking about it."

Southampton boss Ralph Hasenhuttl cut a frustrated figure afterwards, bemoaning the poor defending of his team.

He added: "This game today was a little bit too easy for the opponent. In the other games we didn't give so much chances away, but today it was too easy for them.

"OK we took a bit of a risk with a 4-3-3 and then it's important you have a good start, we had the first chance, but to take the lead at home, it never happens this season so far and that would absolutely help us.

"In total it is not enough at the moment and this is why we will have two intense weeks in front of us."