The Gunners bounced back from a poor start last season to finish in a credible third place, above North London rivals Tottenham Hotspur.
Santos thinks that Arsenal will have higher aspirations this time round and are targeting a first league championship since 2004.
He told Four Four Two: "We shouldn't aim to get closer to the top teams, we have to leave them behind. I think we had a good performance last season, and if it wasn't for that poor start we could have fought for the title.
Arsenal begin their 2012-13 campaign at home to Sunderland on Saturday.