As Kaká stood on the balcony of Milan's offices in Via Turati in September, clutching a familiar red and black shirt and contemplating a new beginning in an old setting, the fans in the street beneath him began to sing. "Siam venuti fin qua per vedere segnare Kaká," they bellowed – "We came here to see Kaká score."

Taken literally, their chorus did not make a whole lot of sense. Kaká did not have space to juggle a ball up on that balcony, much less a net to kick one into. But those words made his heart skip a beat. This was his song, the one that Milan's fans had always sung for him and the one that he loved to hear them sing. The one that told him everything he needed to know: after four unhappy years away, he was finally back home.

It was easy to get swept up in the romance of that moment. Kaká had never asked to leave Milan, famously weeping on the balcony of his own home when the club first considered selling him in early 2009. His affection for this team and this city were sincere, and he eventually left only because the Rossoneri needed the money. His €8m per year salary had become unsustainable, and the €64.5m transfer fee offered by Real Madrid was too big to turn down.

He took a substantial pay cut in order to return, accepting €4m per year this time around – barely 40% of what he had been earning in Madrid. If nobody's heart was exactly bleeding for Kaká over such a financial plight, then his actions nevertheless reinforced the sense that he was moving for love, not money.

But affection cannot turn back clocks, and many believed that Kaká's time as a top-level footballer was already at an end. Although the player was still only 31, he had been a colossal disappointment in Madrid, undermined by recurring injuries and underwhelming when he did get on to the pitch. Somewhere along the way he had lost the change of pace that once defined his game – the ability to accelerate past a defender despite lacking brilliant top-end speed.

In Italy the sceptics dismissed Kaká as minestre riscaldate – reheated soup. Milan's supporters knew from experience that it usually tastes worse the second time around. Andriy Shevchenko had failed to recapture past form when he came back on loan from Chelsea in 2008, just as Ruud Gullit did when he returned briefly from Sampdoria in 1994.

Kaká's first game back reinforced all of the most negative expectations. Despite working hard, the Brazilian made no significant contribution to Milan's cause in a 2-2 draw away to Torino, before hobbling off in the 64th minute. Gazzetta dello Sport awarded him a five out of 10 in their player ratings – the joint-lowest score on either team.

He was subsequently ruled out of for a month with what turned out to be a thigh injury. Kaká was devastated, and immediately announced that he would take no wages from the club for the duration of his absence. But still many people rolled their eyes. The consensus was that Milan had been sold a crock – a player whose body could no longer withstand the rigours of playing at this level.

Kaká knuckled down and got on with it. Despite the injury, he was, according to team-mates, the first man to arrive at their Milanello training base each morning, and the last to leave at night. By the time he returned to action, coming on as a late substitute in Milan's 1-0 win over Udinese, the player looked fitter, stronger and sharper than when he arrived.

His manager, Massimiliano Allegri, took a gamble, starting Kaká in his team's Champions League game against Barcelona three days later. He was rewarded with a decisive performance, the Brazilian setting up his compatriot Robinho for Milan's goal in a 1-1 draw. Kaká would contribute significantly to the team's defensive efforts thereafter, running himself into the ground before his late substitution. "If it helped the team," he said, "then I would even play at full-back."

Anxious not to overwork the player, Allegri left Kaká on the bench for the team's next fixture, away to Parma, but wound up introducing him early in the second half, with Milan down 2-0. Within 12 minutes, the Rossoneri were level, Kaká galvanising their team along with his fellow substitute, Alessandro Matri. But a free-kick conceded in the fourth minute of injury time meant that they still lost, 3-2.

By now Kaká had heard his song many more times, Milan supporters imploring him at each game to give them the goal that they craved. On Wednesday he finally obliged, reopening his account for the club with a sensational strike against Lazio at San Siro. Receiving a pass on the edge of the box near the left-hand touchline, Kaká cut inside before whipping a venomous shot into the far top corner.

If this was indeed reheated soup, then Lazio had tasted it before. Kaká scored a remarkably similar goal against them at San Siro back in 2008. Both were breathtaking finishes; Gazzetta's Nicola Cecere opined that: "Even [Marchetti] would have joined in the applause if he could."

Instead Kaká made do with being hailed by Shevchenko, who had been watching from the stands. "Ricky is amazing," said the Ukrainian. "I'm so happy that he is back."

Milan's joy, though, would soon be tempered by a Lazio equaliser. Kaká's goal had given Milan the lead nine minutes into the second half, but barely a quarter of an hour later Michaël Ciani headed home for the visitors from close range. The game finished 1-1.

It was the latest setback in a deeply disappointing start to the season for Milan, who have collected just 12 points from their first 10 games. They have conceded 17 goals. Only once since the second world war (in 1983-84) have they posted a worse defensive record at this stage of a season.

So exasperated are the club's fans that one of them even tried to sell Allegri on eBay this week, listing the manager at a price of just €1. "We hope you will do us the pleasure of letting us offer you a useless manager who does not know how to manage, does not know how to motivate his players and makes absurd substitutions," ran the product description. "He specialises only in matches against Barcelona. Buy now and receive a free [Mauro] Tassotti."

There have been reports that Allegri will be fired if the club does not climb back into the European places by the end of November – no small task when you consider that they sit seven points outside of the top five (and 13 behind the top three). But it remains to be seen if Milan would actually pull the trigger. Allegri has supposedly been on the verge of losing his job for the best part of two years, and yet he remains in place.

His prospects of surviving this latest round of speculation, though, will certainly be improved if Kaká can continue taking steps towards recapturing his best form. "I went through some difficult moments in Madrid," said the player at full-time on Wednesday. "Now the moment has come for me to rediscover the joy of playing football and having fun on the pitch.

"I'm happy right now, it is a special emotion to be here. I am only sad about the result. The people, the stadium, my chant – these things all give me a special lift, a little something extra."

The feeling is certainly mutual. Milan's fans came to see Kaká score, and he did. Next, they would like to see him win.

Talking points

• Only three teams in Serie A can still boast a perfect home record: Roma, Juventus and … you guessed it, Verona. Andrea Mandorlini's team bounced back from their defeat away to Internazionale at the weekend by recording a fifth consecutive home victory – beating Sampdoria 2-0 through goals from Juan Gómez and Luca Toni. The tendency when talking about this team has been to focus on the brilliant developing talents of players like Juan Iturbe and Jorginho, but really the contribution of Toni should not be underestimated. As well as scoring four times in eight appearances, he also leads the team with three assists. The way that he has led the line, using his strength but also all of his experience to manipulate defenders and bring team-mates into play has been wonderful to watch. There are many richer clubs in Italy and elsewhere who could have used a man of his talents.

• Sticking with old-timers, Andrea Pirlo celebrated his status as the only Italian on the 23-man shortlist to win the Ballon d'Or by scoring the 39th free-kick goal of his career in Juventus's 4-0 rout of Catania. But for his manager, Antonio Conte, the more important achievement was keeping a clean sheet. The Bianconeri had conceded 10 goals in their first nine games, after giving up just 24 in the entire 2012-13 campaign.

• Juventus moved to within a point of the league leaders Roma (who play at home to last-placed Chievo on Thursday evening) and Napoli did the same as they won 2-1 away to Fiorentina. The Viola, though, had cause to feel aggrieved after they were denied a clear penalty in second-half injury time. Instead of being awarded a spot-kick when he was cut down by Gökhan Inler, Juan Cuadrado was sent off by the referee, Giampaolo Calvarese – who believed that the forward had dived. Cuadrado had already been (correctly) booked earlier in the game for simulation.

• The midweek round brought yet another topsy-turvy game for Torino, who led 2-0 at home to Livorno, then collapsed to trail 3-2 midway through the second half, before snatching an equaliser from the penalty spot four minutes from time. These sorts of games are fast becoming the norm for Giampiero Ventura's team, who led twice at home to 10-man Inter, then fell behind 3-2 before Nicola Bellomo brought them level in the 90th minute.

Results: Atalanta 1-1 Inter, Cagliari 0-3 Bologna, Fiorentina 1-2 Napoli, Genoa 1-0 Parma, Juventus 4-0 Catania, Livorno 3-3 Torino, Milan 1-1 Lazio, Sassuolo 1-2 Udinese, Verona 2-0 Sampdoria

• Latest Serie A table