"You don't know what you're doing" is one of the most frequent taunts directed by supporters at referees, managers, directors and anyone else whose decisions meet popular disapproval. Oddly, you never hear crowds follow that up a while later with the admittedly less-catchy chant of: "Actually, sorry about that, it appears you do know what you're doing." Perhaps Southampton fans will be the first?

Then again, perhaps not. But what is clear is that three weeks and three matches after the hugely contentious sacking of Nigel Adkins, the club's new manager, Mauricio Pochettino, is winning admirers. Now all he has to do for the decision to hire him to be vindicated is, well, win matches. There are signs that his team will start doing that soon, perhaps even on Saturday against Manchester City.

Pochettino's team have already given the other Manchester side a mighty scare. In his second match in charge, Southampton outplayed United for long periods, finishing the match with 57% of the possession and twice as many shots as the hosts – but as 2-1 losers.

Sir Alex Ferguson said afterwards that Southampton were the best opponents that his team have faced at Old Trafford this season. Wigan Athletic players expressed similar sentiments after scraping a 2-2 draw at the DW Stadium last weekend. So what has he changed?

The first part of the answer to that is: not that much, because not all that much needed changing at Southampton. The team had played quite well all season and the defensive problems that undermined their fine, attacking play early on in the campaign were already being eradicated under Adkins as he and the players adapted to the Premier League while retaining the qualities that had helped them achieve two promotions in two season.

So there has been no transformation. But there have been tweaks that have made a positive impact. The Argentinian speaks only sketchy English but has had no problem conveying his message, partially because all three of the coaches he brought with him speak English fluently and partially because his message is not that complicated.

The main change he has made is to make the team more aggressive without the ball, encouraging them to harass the other side into coughing it up as close to their goal as possible and then, with the opposition ragged, Southampton are told to use their forward flair to take advantage quickly.

"Our style of play is to win back the ball as soon as possible and then play it," the manager explains. "We moved forward our lines and play more upfield. When we lose the ball we must have the mentality of winning it back as soon as possible."

That is how Espanyol played during the three and a half years for which Pochettino kept the club higher than their resources should have permitted, earning admiration for his tactics from Pep Guardiola among others, before the consequences of continually selling their best players finally caught up with them.

Espanyol players nicknamed him "The Sheriff" and used to talk of training sessions that were fiercely "intense" yet "fun".

Southampton players have expressed the same view, which is just as well, as Pochettino has treated them to double sessions since his arrival. It is not simply fitness work – in fact, he has no quibble with the level of fitness that he found and so far the focus of training has been on ensuring there is a solid structure to the way the team press.

"It may seem like we are running more," he says. "But really we are just running in a more organised way."

One player who certainly looks like he runs more is Morgan Schneiderlin. The central midfielder has always been a dynamo and has made more tackles and interceptions this season than any other player, but under Pochettino he, like the full-backs, has also been ordered to attack more, a mission that is, of course, easier to accomplish if Southampton win the ball high up the pitch. His goal against Wigan, when he sprinted 50 yards forward before slamming in Gastón Ramírez's cross from close range, could become a regular feature.

"I like midfielders who cover a lot of ground and go into the opposing team areas," says Pochettino. "We ask players to do what they are capable of doing and both Jack [Cork] and Morgan have a great capacity in that respect so we ask them to use it."

With Adam Lallana now sufficiently recovered from injury to challenge for a starting position, City are in for a serious test. They are the sort of team that Southampton aspire to beating on a regular basis. The executive chairman, Nicola Cortese, is unashamedly demanding with his targets and envisages achieving more than mere survival in the Premier League. To him the dismissal of Adkins is a reasonable form of ruthlessness, since he believes that while Adkins may have kept the team up, Pochettino can take them higher.

The new manager helped embed that notion before the United match when he took the squad to work out at Barcelona's training ground for a few days. Premier League players may have more wealth than they can dream of, but using the same facilities as Lionel Messi et al is one way they can still be wowed. It is clear from talking to Saints players that the experience helped persuade them that their manager is big time. They need to start winning to convince everyone else that he came at the right time.