The 29-year-old finished with 16 Premier League goals this season.
The Frenchman put a very mixed season to one side this afternoon by scoring a hat-trick in the 4-0 demolition of Aston Villa as the Gunners pipped North London rivals Tottenham Hotspur - who lost 5-1 at 10-man Newcastle United - to second place in the Premier League.
The 29-year-old also scored in last week's 2-2 draw at Manchester City for what was his first goal in 15 league games, his barren spell coinciding with Arsenal's title bid petering out for a 12th successive year since 2004.
And Kilbane has suggested that the France international does not inspire confidence in him that he can fire the North Londoners to Premier League glory any time soon.
"He probably isn't [a top striker] if the truth be known. I don't think he does enough in those big games, in those defining moments of a season," he told BBC Sport.
"He went 14 (15) games without scoring a goal and that was the problem," ex-Arsenal defender Keown added. "Too many of the Arsenal team lost their form at a key point in the season."
Giroud finished with 16 Premier League goals in 38 appearances - 26 starts - which, for a club like Arsenal, is not good enough.
He certainly deserves a spot in Arsene Wenger's squad next term, but he is not the forward they need if they're hell bent on winning the biggest prizes.