The latest attempt to offer an explanation for uncalled-for behaviour was posted at around 4.45pm last night on Arsenal's official website. Cesc Fábregas's statement mentioned an underlying "respect" for the officials and an all-consuming passion for a club embroiled in the title race, but was less an apology and more an admission that, as he put simply, "so many things are said in the heat of the moment".

The storm in a teacup this time was a reaction to his team's half-time deficit to Everton on Tuesday night which the visiting manager, David Moyes, branded "disgusting" in his post-match analysis. Some of those who had witnessed his outburst claimed Fábregas had shouted "How much have you been paid?", apparently to no one in particular, as he jogged down the tunnel towards the dressing rooms. The referee Lee Mason either did not hear or did not feel the home captain was venting his spleen at the officials, so no sanction will be imposed by the Football Association. Regardless, the fierce competitor in Fábregas is tarnishing his image these days.

That much is regrettable. The 23-year-old World Cup winner is such a magical footballer to watch, his vision and delivery of pass and shot invariably thrilling and undoubtedly inspiring a team that are thriving on four fronts. But too often these days it is the memory of his spikiness that lingers after contests. Against Ipswich and Huddersfield Town in recent and distinctly awkward ties in the Carling and FA Cups, he had infuriated lower league opponents as much with his attitude as with his sublime creativity. As club captain, and a figurehead ambassador for a youthful squad, he should surely be better than that.

There was a lack of dignity to his ungracious post-match assertion that Ipswich had resorted to "rugby" kicking to establish an unexpected first-leg lead. The Terriers' midfielder Anthony Pilkington turned to Twitter, on which Fábregas's followers total almost 378,000, to brand the Spaniard a "sick player but what a tit" on Sunday. That related to a squabble over which Huddersfield player would claim his shirt at the final whistle, though the visitors' heckles had already been raised by his waving of an imaginary card at Mark Clattenburg when Jamie McCombe fouled Nicklas Bendtner to earn a late penalty.

There was little dignity to either spat, but the reality was that listening to Moyes condemn Fábregas's behaviour on Tuesday felt far too familiar, as if he was complaining about a petulant teenager who felt he was untouchable. For Moyes, read Mark Hughes some four years ago when the Spaniard left the pitch at Emirates Stadium after a bruising 0-0 draw to shake hands with the then Blackburn Rovers manager and ask whether Hughes had played for Barcelona. "When I said yes, he shook his head as if in disbelief," recalled Hughes. "Then he said: 'Well, that wasn't Barcelona football.'" Arsène Wenger had offered a rebuke at the time. "I went to the dressing room to make my apology to him," said Fábregas subsequently. "I am very young and still have a lot to learn."

Then, infamously, there was the injured midfielder's appearance on the pitch, dressed in a hoodie, jeans and trainers, in March 2009 after a fractious FA Cup quarter-final win over Hull City and, within minutes, accusations from the visitors' manager, Phil Brown, that Fábregas had spat at his assistant, Brian Horton. Claim and counter-claim followed, but no disciplinary action was taken due to insufficient evidence. The infuriation, again, was that the whole incident had been so unnecessary.

As a result, the fresh-faced image promoted by the brilliance of his football and his eloquence off the pitch has steadily been cast aside. The midfielder dazzles on the pitch arguably brighter than ever before, the personification of the style and panache his team attempts to conjure. But the flipside is that few eyebrows are raised, for example, when Roberto Martínez accused him of "buying" a penalty by drawing a foul from Gary Caldwell at Wigan last month. "Cesc comes from a different culture: that action in Spain gets a 'well done' from everyone," said Martínez. "In England, to do that is cheating."

His manager, who has cultivated the midfielder's competitive streak, and his team-mates still rejoice in the power and presence he offers. Jack Wilshere, a young midfielder who has developed his game in Fábregas's mold, turned on the radio yesterday to hear his captain being criticised and promptly tweeted his support. "He is a brilliant leader and protects his team-mates always," he wrote on Twitter. "A very passionate guy." Perhaps it is that passion that is landing him in trouble. At 23, he is still so young but he is a player around whom Arsenal's very hopes are built. The pressure of that expectation, and his desire to succeed having claimed only the 2005 FA Cup to date, can coax the best out of him, but there is a dark side to his game that clearly rears too often as well. Plenty of people within the game admire his ability. Fewer appear to be warming to his personality.

• This article was amended on 3 February 2011. The original referred to Fábregas having left the pitch at Ewood Park some four years ago. This has been corrected.