While the loss of Holland striker Van Persie for at least six weeks with ankle ligament damage is a major blow, Wenger knows it could have been much worse.
Wenger said: "We knew when Robin came out with this injury that he would be out for a long time, but frankly I feared it would be more because the first news was very, very bad. So it was a relief that he would be out for six weeks.
"Of course it is a disappointment and something we did not want, but I feel we have enough strength to compensate for his absence for a while.
"It will also allow him to be fresh for when he comes back."
On the subject of Kieran Gibbs, he added: "Our medical staff called me saying he was in hospital in Lithuania with a suspected broken metatarsal.
"Later on, it was much better news.