Arsenal manager Arsene Wenger sarcastically mocked Nani after the Manchester United winger dismissed the Gunners' Premier League title bid.
The Gunners sit second ahead of Monday's London derby with fellow title hopefuls Chelsea at Emirates Stadium.
But Nani believes United, who lead Arsenal by two points with a game in hand, only need to worry about the challenge of Chelsea.
Gunners boss Wenger, who began his managerial career with Nancy in 1984, is not impressed by the Portuguese winger's comments and has implied his side are more than capable of winning their first league title since 2004.
"Everybody has a different opinion in this league and nobody is perfect," the 61-year-old told Sky Sports News.
"We live in a society where everybody knows everything and it is a shame to say, 'I don't know'.
"I personally don't know who will win the league and I have managed 1,600 games. If Nani knows he must be 1,600 times more intelligent than I am."
Arsenal have not won a trophy since the 2005 FA Cup and have faced the usual accusations of naivety this season after already losing five league games and failing to live up to expectations on the big occasion.
Wenger has persistently defended his players and he thinks that an apparent inability to deal with pressure is a common trend in England's top flight.
The Frenchman said: "We have seen recently that any team, when they think they are on the brink of breaking through, they have the hiccups.
"Maybe it is just the quality of the league?"
Arsenal have had to cope without star centre-back Thomas Vermaelen since September, when the Belgian sustained an Achilles injury.
But Wenger is optimistic the £10million arrival from Waalwijk in 2009 will be fit for the first team early in the New Year.
The Arsenal boss said: "He has been out for a long, long time. We are hopeful that he we will be back in January."
