The Holland striker - whose 30 goals had dragged the Gunners into third place in the Barclays Premier League last season - on Friday completed a £24 million move to Manchester United, having made it clear earlier in the summer he would not be signing a new deal.
Wenger's side - boasting summer signings Lukas Podolski, the German striker, and impressive Spain midfielder Santi Cazorla in the starting XI - enjoyed plenty of possession, but failed to find a telling pass to open up a stubborn Sunderland rearguard.
When a clear opening eventually came their way late in the second half, substitute Olivier Giroud, who netted 21 goals for Montpellier last season, fired wide.
"We played with a good spirit, were serious and we put the effort in, but we lack sharpness and fluency at the moment to be dangerous in the final third," said Wenger.
"The few chances we had, we could not convert them.
"Sunderland defended very well for the whole game, and we lacked something - sharpness, also quality and accuracy in the final pass."
Wenger added: "The formula didn't work with three strikers up front and we were not well balanced, we did not create enough because they blocked our midfield."
Cazorla, however, showed he could well prove to be one of the signings of the summer having joined from Malaga.
The Spain international almost opened his Arsenal account in the first half, when a fierce 20-yard drive was saved by Simon Mignolet.
Wenger said: "It is difficult not to be pleased with him because he played on Wednesday night, the whole [international] game in Puerto Rico.
"All the chances were created by him, basically."
The Arsenal manager, however, rejected suggestions Van Persie would have won them Saturday's game.
"You can never check that. We have played some draws at home with Van Persie, we have lost some games with Van Persie as well," Wenger said.
"However, it is true that last year in every game he found something special.
"I never denied that we lost a world-class player, that is very difficult to replace."
Arsenal on Saturday night announced terms had been agreed with Barcelona for the transfer of midfielder Alex Song, believed to be as part of a £15million deal.
"He expressed a desire to go to Barcelona," Wenger said.
"It is frustrating, we have learnt to deal with that.
"I believe as well that the financial potential of some clubs is massive and that makes a difference."
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Wenger, however, feels Arsenal have enough cover in midfield.
"We have [Jack] Wilshere coming back, I believe in one and a half months. We have [Abou] Diaby back, we have [Tomas] Rosicky not far away and we might bring another midfielder in as well."
Arsenal have also been linked with Real Madrid's Turkey international Nuri Sahin.
Wenger, though, said: "You have to be patient a little bit [over any new signings]."
Denmark striker Nicklas Bendtner is also expected to leave ahead of the transfer deadline.
However, Wenger played down reports the player was set to move to Italy next week.
"Bendtner is likely to move, yes, but there is no deal done at all," he said.
For Sunderland manager Martin O'Neill, it was a point earned on the back of what had been an energy-sapping display in sweltering temperatures.
"We were very tired from about 65 minutes onwards, but that game will bring us on immensely," said O'Neill, who hopes to bring in some more new players ahead of the transfer deadline.
"We have not been able to get our squad up to strength and I knew coming here was going to be difficult.
"We ran out of energy towards the end and we hanging on, but at least we are off the mark."
O'Neill added: "We should have done better in the first half, James McClean had a shot and Jack Colback got himself into a good position too, but in the second half Arsenal had most of the possession and we had to defend."