Van Persie helped Wenger's side qualify for the group stages of the Champions League with a vital equaliser in Wednesday's 2-1 victory over Udinese in Italy.
But the Dutch forward knows Wenger's inexperienced squad still has room for significant improvements following the recent sales of star midfielders Cesc Fabregas and Samir Nasri.
"It's vital for Arsenal (to make signings)," he told Sky Sports News. "Of course we did lose Samir and Cesc which is very hard for us because those are two great players."
Although Van Persie, who took over the captain's armband after Fabregas's departure, would like to see several new faces arrive over the next week, he still has faith in his young team-mates and praised the way they fought back from a goal down to beat Udinese.
He believes the future is bright for the club with the likes of Carl Jenkinson, Emmanuel Frimpong and Wojciech Szczesny, who saved a penalty, all performing with distinction against the Italians.
"To come up with that performance in the second half is special. If you look at our team and people did question our mental strength. We've shown loads of that," Van Persie said.
"Carl Jenkinson for example, I think it was his best game so far. We played really well. Szczesny is on fire. He saves almost everything.
"Frimpong is doing well. I'm just happy that we're in it and let's go from there."