Ole Gunnar Solskjær urged Manchester United supporters to retain belief in his methods after his side stuttered to a draw against 10-man Southampton but conceded they must rediscover a ruthless streak after extending their winless away run to eight Premier League matches.

Solskjær also confirmed Paul Pogba will remain at the club beyond Monday’s European transfer deadline but the problems run deeper for United, who have won one of their past nine league games. They have not triumphed on the road since Paris Saint-Germain in March and the manager admitted his team remain a work in progress.

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“We have dominated the last three games and we know we are on the right track, we’re getting used to that way of playing,” said Solskjær, who has not tasted victory since the opening-day victory over Chelsea at Old Trafford.

“The last three games, they haven’t given us many points in return but we are getting there, we’re getting better and better at playing this way. It is a young team that will get used to it. We need to be more clinical, more ruthless when we go forward but we gave them enough encouragement to stay in the game.

“We are dominating and creating chances but haven’t been clinical enough in front of goal to win. We have missed penalties, chances – it’s a dip in results but not in form.”

Pogba twisted his ankle late on but Solskjær said he expects the France midfielder to go away on international duty. “We, as a team, started giving sloppy balls away after about half an hour and Paul was one of them, but he wasn’t different to anyone else,” said the United manager. “Everyone expects everything from him every game – he has to attack, he has to defend, he has to win headers, he has to win tackles, he has to dribble past people, he has to make passes – that’s just Paul, and he will thrive on that.”

Solskjaer’s confidence is somewhat reassuring given the manner that a game that started so promisingly following Daniel James’s emphatic opener slipped away from United, with the 6ft 6in Southampton defender Jannik Vestergaard towering above Victor Lindelöf to nod in a cross by Kevin Danso, who was later sent off after picking up two yellow cards – the second of which was reckless – to earn parity.

James’s performance was heartening and his return of three goals in four league games translates to having the same tally of Premier League goals in a United shirt as Alexis Sánchez.

The visitors peppered Angus Gunn’s goal late on, with 17-year-old Mason Greenwood, Jesse Lingard and Ashley Young going close from distance without finding a winner. United could have been out of sight, with Marcus Rashford squandering two clear sightings of goal, but it was a flaky performance at best.

Facebook Twitter Pinterest Kevin Danso makes his ill-conceived challenge on Scott McTominay. Photograph: Will Oliver/EPA

Solskjær acknowledged United are light on numbers with Romelu Lukaku and Sánchez departing in the past week, increasing the onus on Rashford to deliver – and while the striker’s work-rate was admirable, he badly fluffed a first-half header.

Solskjær is not concerned the forward is overburdened and, in fairness, his three summer signings – James, Harry Maguire and Aaron Wan-Bissaka – again looked the part. James’s performance was an overwhelmingly positive takeaway. His 10th-minute opener was magnificent, an unstoppable strike that soared into the roof of the net after Cédric Soares allowed him to jink inside on to his right foot, and the 21-year-old could have doubled his and United’s tally had Oriol Romeu not stepped in to stop a later chance.

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Juan Mata also began brightly on his first start since May but his influence diminished as Southampton, kept at arm’s length for long stages, sensed a degree of vulnerability.

Che Adams skewed wide after being played in by Sofiane Boufal before Danny Ings forced a save out of David de Gea. United failed to extinguish the danger, Southampton recycled possession and suddenly they were level, as Danso picked out Vestergaard, who headed beyond De Gea.

“It’s an unbelievable performance mentally from my team and I can only raise my hat to them,” said Ralph Hasenhüttl. “They [United] never got in the rhythm in the second half and then we got the equaliser.

“I believed maybe we could even get three points but the red card ended that.”