Star striker van Persie scored 37 goals in all competitions last term but left to join top-flight rivals Manchester United in a reported £24 million move.
Wenger saw his side struggle in the attacking third of the field against a determined Stoke at the Britannia Stadium on Sunday but remains confident that Lukas Podolski, Olivier Giroud and Gervinho, supported by attacking midfielder Santi Cazorla, will eventually all come good.
"The understanding was missing," said Wenger. "One month ago Cazorla and Podolski did not know each other. There is work to be done on the training ground. There is potential but something is missing.
"I am very positive about my team. We haven't scored in two games but we played against two units that defended very well."
The Frenchman added: "If you want to convince we've lost an exceptional player you are wasting your time. I was the first to say that. We must find a way around that by sharing around the goals we scored with van Persie.
"I've worked for 30 years on the football pitch every day and I know what it takes to improve a football player.
"Giroud can't think like he should replace Van Persie. I had the same questions when Thierry Henry left. We have to take perspective."
Wenger felt both Stoke and Sunderland, Arsenal's opponents the previous week, played overly defensive line-ups to nullify the Gunners' attacking threats.
"I feel we played against two highly focused defensive sides. Other games are more open. Some other teams go forward and open their games.
"The teams we played against like it was a cup final for 90 minutes. But we behaved like men who were ready for a fight.
"Offensively we have some work to do as we missed accuracy in the final third. We should have won the game 1-0 but credit to Stoke, they defended really well with experience at the back.
"Defensively we had no problem, they had one good chance in the second half but apart from that we did very well. If they have six basketball players at set pieces, it's very difficult!"
Wenger's opposite number Tony Pulis was delighted with Stoke's second draw of the season.
"I'm really pleased with a point," he said. "But we were disappointing going forward and looked unbalanced. The attitude was first-class. As a football club we must never become blase."
Pulis hopes to sign Maurice Edu from Rangers and complete the loan signing of Tom Huddlestone from Tottenham on Monday.
Another Tottenham player Michael Dawson is also a possibility but Pulis will not risk the club's financial stability in a bid to bolster his squad.
"We'll know about a couple of players on Monday -- I hope it will be a busy week for us as it will freshen us up," he said.
"We have to do it in a more structured way this year. We have just got category A with the academy and have a setup.
"The chairman (Peter Coates) is a local lad and we hope it will be a system that brings through young players. The Coates family want local youngsters to give their all for this football club.
"I'd like to take Dawson at Spurs but I don't know if we can afford it. But you have a level on who you can bring in. If we have to bite the bullet, we bite the bullet."
Source: AFP
Source: AFP