Forward Antonio, who had a second-half goal disallowed by VAR for handball, was a constant menace to Southampton's defence and believes his team have sufficient desire to rediscover their early-season promise.

"Obviously we showed in our performances in the last couple of weeks we've improved, but we haven't got the results we wanted," Antonio told West Ham's website.

"But we showed that we've got the fire, that we've got the grit.

"It was a massive result because we've got loads of respect for the manager.

"We started the season well before we went on a bit of a blip.

"I've been here for five years now and we've always come out of these blips. Hopefully this is the time where we can start moving forward and getting ourselves up the league."

West Ham's record signing Haller had gone eight top-flight games without a goal before scuffing home his fifth of the campaign in the 37th minute.

Antonio was unfortunate not to double the advantage when his crisp second-half strike at the end of bundling run was ruled out following consultation with Stockley Park.

Pellegrini was pleased to see his side beginning to fulfil their potential and is looking forward to an 11-day break ahead of three games in seven days, starting at Crystal Palace on Boxing Day.

"I don't know exactly if the word is relief. For me seeing the team playing the way we did is what I expect about us," the Chilean said of the much-needed win.

"I'm always talking with the players that we must play the same way we work every day of the week, we must try to be a solid team and score goals and I think we are able to do it better.

"After a couple of days off, we will recover and start preparing for the game against Crystal Palace.

"It is a part of the year where I think we must arrive fresh because we play 26, 28 and the 1st."

Southampton failed to build on successive home wins over fellow strugglers Watford and Norwich, suffering an eighth defeat from 12 league games.

Saints boss Ralph Hasenhuttl opted to substitute under-performing winger Nathan Redmond at half-time.

Redmond was rejuvenated by Hasenhuttl's arrival last December and named the club's player of the year for 2018-19 but has struggled to replicate that form this term, scoring only once in 15 league appearances.

"The subbing in half-time was not only about a bad performance, we changed the shape," said Hasenhuttl.

"Sure, in the moment he is missing a little bit the goal maybe, he had the chance against Newcastle (on December 7) and then he maybe would have been more self-confident.

"But he must work, like we all have to do it. In the end, it's about getting the next chance and showing up."

Saints travel to 17th-placed Aston Villa next weekend and Hasenhuttl is optimistic about a positive response.

"We know that we can take something against Villa so therefore we should take the heads up and look forward," he said.