Following his move to West Ham this week, Ljungberg argued his former club lacked ambition and their glory days were over.
But French defender Clichy said: "I don't think Arsenal lack ambition.
"We know we've got the quality, the strength. Everyone is confident, we have signed new players and we are going to have a great season.
"For two years we hear Arsenal are not competitive any more but last season we won both matches against Manchester United, drew both against Chelsea with what is supposed to be a young team, so I don't know what's wrong with that.
"We have a few new players who have added more quality to the team and the boss is one of the best managers."
Arsenal's already youthful squad is even more inexperienced following the departures of Ljungberg and Thierry Henry but Clichy does not seen it as a problem.
He said: "Of course it is difficult to lose a player like Thierry, who is one of the best strikers in the world. But I think we have plenty of qualities, everyone can see it, and I think this year will be a big one for Arsenal."