The Gunners kicked off the new campaign with a frustrating goalless draw against Sunderland on Saturday, with new strikers Lukas Podolski and Olivier Giroud unable to provide the firepower that Van Persie so regularly delivered last season.
Arsene Wenger has insisted it would be unfair to make judgments after just one game, while Cazorla is also confident the team will improve as the season develops.
However, the Spaniard admits it is disappointing that Van Persie has joined Manchester United and Song is set to complete a move to Barcelona after a deal was agreed over the weekend.
Cazorla said in the Daily Mirror: "It's clear that Van Persie is a great player and obviously we would all have preferred it if he had stayed. Song has gone as well and there are still 10 days left in the transfer market.
"I do not know if we will sign anyone but obviously it's important to replace players like that because they were so important for the team."
While Arsenal did not get the victory they were looking for against the Black Cats, Cazorla caught the eye with an impressive performance in his first appearance since arriving from Malaga.
He said: "It felt really good making my debut. Of course, it was not the result any of us wanted, but we had chances and we did well.
"It's a long season, so we can build on this. I had one chance and so did a few of my colleagues and that was the key to the game. We had complete control but that final step just eluded us."
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