He is unlikely ever to admit it, but a few alarm bells must have been ringing inside Mauricio Pochettino’s head when Stoke City left White Hart Lane 2-1 victors on 9 November. It had not taken long for Tottenham Hotspur to lose four home matches in the league, they were off the pace in the race to finish in the top four and, knowing how short Daniel Levy’s patience can be, there were a few mischievous whispers about Pochettino potentially being in trouble. This is modern football; someone, somewhere, has to be in crisis.

That would have been ludicrous short-termism given that Pochettino had only been in the job for a few months after leaving Southampton last summer and now, allowed time and space to get his message across to his players, he has lifted Tottenham to fifth place. They have lost only once in their past nine league matches – and there were actually some encouraging signs from Tottenham in the first 20 minutes of what ultimately turned out to be a comfortable 3-0 victory for Chelsea at Stamford Bridge last month – and they will go fourth if they beat Crystal Palace at Selhurst Park on Saturday. Southampton, who are two points above Tottenham, visit Manchester United on Sunday.

Pochettino deserves praise for the speed of Tottenham’s improvement. He did not use the Europa League as an excuse for Tottenham’s poor home form, even though those four defeats had all come after their Thursday night adventures, because he knew that his team should have been good enough not to lose to Liverpool, Newcastle United, Stoke and West Bromwich Albion at White Hart Lane. He knew that something was wrong and that the malaise could not continue indefinitely, so he did not hold back after the Stoke game. “We need to improve a lot,” Pochettino said. “We need to improve quickly. You never have a lot of time in football. We need to find a solution and change mentality in the next few weeks. That is my challenge.”

It was not the first time we had heard a Tottenham manager speak about the need for his players to develop stronger characters. It was a familiar refrain from Tim Sherwood last season, most famously when he blew up after the 4-0 capitulation at Chelsea last March. Yet Pochettino, even with his broken English, has a lighter touch than Sherwood.

Southampton’s players liked and respected Pochettino, although it is worth remembering that it took a while for him to get going when he arrived at St Mary’s two years ago. There were splendid victories over Chelsea, Liverpool and Manchester City in his first two months, but the only other win came against a doomed Reading side and Southampton finished 14th. They were winless in their final six matches and they had a couple of dodgy results at the start of last season too, struggling for ideas and inspiration in home draws with Sunderland and West Ham United.

By the end of September, though, Southampton were fully starting to feel the Pochettino effect, defending well, pressing high and attacking with creativity and speed. Tottenham liked the look of him.

The best of Pochettino’s football has only been seen in fits and starts at Tottenham. There was a glimpse of it in the 4-0 thrashing of Queens Park Rangers in August and then when they roared back from a goal down to beat Everton 2-1 at White Hart Lane at the end of November, but it was against Chelsea on New Year’s Day that the Tottenham fans really saw what Pochettino wants from his side. It was a day when just about everything came together, despite the three goals that Chelsea put past Hugo Lloris, as Tottenham overwhelmed José Mourinho’s side with the intensity, energy and focus of their play, winning 5-3. They were a blur of motion during that thrilling period towards the end of the first half when they stunned Chelsea by scoring three times and there were some excellent goals from Nacer Chadli and Harry Kane. The last time a Mourinho side conceded five in one match? When Barcelona beat Real Madrid 5-0 in November 2010.

It is, of course, impossible to get through this article without talking about Kane. Pochettino was not alone in not seeming convinced by him at first but the failure of his expensive strikers, Emmanuel Adebayor and Roberto Soldado, to make an impact forced his hand and Kane has been a revelation since breaking into the side. He is such an eager cult hero that even supporters of Tottenham’s rivals are probably secretly enjoying his metamorphosis from 21st century Rory Allen to unstoppable Premier League striker.

Kane’s form has been outstanding, but others have made important contributions. This is a Tottenham team without an obvious star – there is no one in the class of Gareth Bale or Luka Modric – but, increasingly, there is a crucial lack of ego and a greater togetherness. Pochettino has always placed his faith in youth and Nabil Bentaleb and Ryan Mason have formed an excellent, forceful partnership in midfield after displacing Mousa Dembélé and Paulinho, while Jan Vertonghen and Federico Fazio are starting to develop a greater understanding. Andros Townsend, previously out in the cold, has looked revitalised in recent weeks after Erik Lamela’s injury gave him a chance.

Lamela has also been more dangerous this season, while Chadli and Christian Eriksen have added consistency to their games. Chadli and Eriksen have been accused of drifting through games in the past, of not accepting enough responsibility, but there has been more of an edge about them this season and they have both scored seven league goals. That is a fine return when compared to their equivalents at rival clubs: Alexis Sánchez has scored 10 goals for Arsenal, but Alex Oxlade-Chamberlain and Santi Cazorla have scored one and four goals respectively, Manchester United’s Juan Mata has five goals, Southampton’s Dusan Tadic and Sadio Mané have two and five goals respectively, West Ham’s Stewart Downing has four goals and Adam Lallana and Raheem Sterling have four apiece for Liverpool.

Tottenham have had to ride their luck at times. It would be disingenuous for them not to admit that they have been fortunate in several matches and they have been indebted to the saves of Lloris on many occasions. Yet, unlike last season, they have not folded at the first sign of trouble and they have shown their grit by scoring late winners in five away matches. It started with Eric Dier’s last-minute winner on the opening day at West Ham, when Tottenham played the majority of the match with 10 men after Kyle Naughton was sent off in the first half, and continued against Aston Villa, Hull City, Leicester City and Swansea City. Pochettino is instilling more resilience.

This being Tottenham, there is every chance their world will come crashing down around them sooner rather than later, perhaps when the Europa League resumes, and just their luck that they get to face Palace in Alan Pardew’s first match at Selhurst Park. Yet they are not such a soft touch these days and with neither Arsenal nor Liverpool in great shape, Tottenham’s quiet rise could lead to noisy celebrations come May.