The Gunners climbed to the top of the Barclays Premier League table on Saturday after a 3-1 victory at Sunderland.
Wenger later revealed that the Spaniard is out of Wednesday's Champions League clash with Marseille and is unlikely to play again before the next international break, and with Lukas Podolski currently also on the casualty list, he admits he cannot afford to lose any more attacking players.
The Frenchman told the BBC: "We score because we have a good game, lively with a lot of energy, we are dynamic in our game, and a lot of belief as well.
"But we are still short now. With the injuries we have, we cannot afford now to lose players."
Despite arriving at the Stadium of Light without defender Per Mertesacker and with record signing Mesut Ozil having only just recovered from the same bug which prevented his team-mate from travelling, the Gunners turned in a superb first-half display and should really have had the game won by the break.
Ozil took little time to settle into his new surroundings, expertly controlling Kieran Gibbs' long ball before sliding a cross into the path of Giroud's run and watching the striker nonchalantly guide it past keeper Keiren Westwood with just 11 minutes gone.
Indeed, Walcott might have had a hat-trick inside the opening 43 minutes, but ended the half empty-handed when he sent a diving header wide from Giroud's cross.