The Black Cats have struggled for top-flight survival during the past four seasons and have lost their opening two Premier League games.
"There have been managers come and gone and everything has been very close to the bottom every season," said Moyes.
"I've said I want to change that but I can't do that overnight."
Moyes took over from Sam Allardyce at the end of July and has had limited time to strengthen his squad.
They lost 2-1 at Manchester City on the opening day of the season and were beaten by the same scoreline at home to Middlesbrough on Sunday.
The former Preston, Everton, Manchester United and Real Sociedad boss says he would "like to get a few" more players in but has "got a lot of work to do with the players".
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"I've told people that it was always going to be difficult," added the Scot, whose side play Shrewsbury in the EFL Cup on Wednesday (19:45 BST).
"I think I said when we came we were always going to build. I've come in late on, it's never going to be easy.
"I hope I was being realistic. There was no point in me telling people untruths - I wouldn't do that. Do we want to be there? No."
The Black Cats' past four seasons have seen them finish 17th, 14th, 16th and 17th - often staying up thanks to late rallies. The 2010-11 campaign was the last time they did not change managers during the season.
Moyes added: "The fact of the matter is we need to make improvements. We need to get more players in, we need to add to the squad."
Meanwhile, Sunderland keeper Vito Mannone has been taken to hospital after injuring his arm in training.
The 28-year-old Italian, who has played in both of Sunderland's game so far this season, suffered the problem during training.
Sunderland manager David Moyes says he was being "realistic" when he told the club's fans to prepare for another relegation battle.