Former England off-spinner Swann, now a commentator with BBC Radio's Test Match Special, said Monday that England "do not have a cat in hell's chance" of winning the World Cup in Australia and New Zealand early next year.
He also urged Cook, whose orthodox approach many pundits believe is ill-suited to the white ball game, to quit one-day cricket completely.
Until December, Swann was a team-mate of Cook before dramatically retiring during England's 5-0 Ashes hammering in Australia.
And coming towards the end of a season where several former England captains said Cook should resign as Test skipper, only for both he and the team to recover to beat India 3-1, Swann's comments did not go down well.
- 'Not helpful' -
"I don't think it's that helpful - especially from a so-called friend," said Cook.
"He's entitled to his opinion. (But) it's not ideal for me, especially when you get through the summer I've had," the 29-year-old Essex left-hander added.
Meanwhile Cook, whose self-confessed stubborn streak saw him continue as Test captain, was adamant he would lead the team at the World Cup, where England will try to lift the trophy for the first time in 40 years of trying.
"I am a little bit (disappointed) - because he (Swann) is a good friend of mine, and has been a supporter," Cook said.
"It's not helpful at this time, because I am going to be captain in this World Cup."
However, Cook accepted England would need to improve vastly on Wednesday's lacklustre effort if they were to be World Cup contenders.
"Obviously, if we play like that we're not going to win many games of cricket.
"But the talent in the changing room is there..It's frustrating. We weren't quite at the races and I don't quite know why."