While United boss Sir Alex Ferguson and his City counterpart Roberto Mancini were trying to ease the tension ahead of Wednesday's semi-final second leg and Carlos Tevez's return to Old Trafford following his bust-up with Gary Neville, Cook was in typically belligerent mood as he addressed a fans' forum in a New York bar.
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To the delight of supporters at the Mad Hatter Saloon, Cook clutched a microphone and said: 'This football club will be without doubt the biggest and best in the world.
'People don't like to hear it but I'll make no excuses for saying it, and I will never stop saying it because I truly believe it with the resources and capabilities that we have - and when, not if, we're at Wembley having beaten Man United yet again!'
It is not the first time Cook has been outspoken in public, having famously accused AC Milan of 'bottling' Kaka's transfer a year ago and then launched into an angry outburst after fierce questioning at Mancini's unveiling last month.
The comments will also concern the FA, who have joined Greater Manchester Police in appealing to both clubs to show greater restraint after trouble flared before and after City's 2-1 win in the first leg at Eastlands on Tuesday when rival fans hurled missiles at each other inside the stadium.
The ill feeling between the players came to a head when Tevez goaded Neville after scoring the first of his two goals, and the United captain responded with a one-fingered gesture.
Tevez has since branded Neville 'an idiot' and 'a creep' for supporting Ferguson's claim that the former United striker Hodgsonwas not worth his £25m transfer fee to City.
Mancini tried to play down the controversy yesterday, claiming Tevez was tired when he made the comments in a South American radio interview. The City boss said: 'It can happen sometimes because players are nervous and tired and don't think after the match.
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'Carlos said that yesterday but it is important for me that it is finished and it is finished now.
'I hope there will not be any trouble at Old Trafford but sometimes it's possible.' Ferguson yesterday insisted he had no problem with Neville's conduct, claiming he had not seen his captain's reaction as he warmed up on the touchline, and deflected questions over Tevez.
'I'm not interested,' he said. 'He's not our player any more, so I have nothing to say about it.'
But the United boss appeared to aim a dig back at City over their lack of big-match experience, saying: 'We are used to big games.'
Tevez has been given the choice of staying at home or taking a place on the bench for tomorrow's FA Cup fourth-round tie at Scunthorpe after suffering a muscle strain against United.
Mancini will rest several other senior players ahead of Wednesday's second leg, when Emmanuel Adebayor could also return after flying back into the country tomorrow following the Togo terrorist attack.
City face an awkward trip to Glanford Park tomorrow, and Mancini has warned his players to heed the lesson of United's shock exit to Leeds in the last round. He said: 'We must remember Liverpool versus Reading and United versus Leeds if we think it will be easy.'
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