Financial restraints at Goodison Park have meant the Toffees boss has been unable to bring in any new players.
But he has had to watch the clubs who finished below them last season make considerable investment.
"I think we are going to have a big struggle to finish in the top 10 this season," said the Scot, who is preparing for a delayed start to the season against newcomers QPR after last weekend's opener at Tottenham was postponed because of the London riots.
"My hope is to do as well as we can. It is well-documented what has happened in terms of clubs buying to improve and I don't just mean the top clubs.
"I can see the likes of West Brom, Stoke, Fulham and Sunderland have all tried to improve and the reason they have done that is to finish where Everton can.
"We have tended to be somewhere fifth, sixth, seventh over the last five years.
"We have to aim to do that if we can but I think it will be tougher for us this season.
"Last season I had higher expectations so maybe people think we have dropped expectations - but when they do that we tend to do better.
"But (repeating last season's) seventh place will be a tough finish looking at it right now.
"I am incredibly ambitious and want to win something with Everton.
"If we can get the players I have brought here firing we have a good side."
After falling a match behind their rival Moyes said his players were raring to go after a hastily-arranged friendly against Bohemians in Ireland on Monday helped some players with their fitness.
"The players are ready to play. We had some who needed the extra week to get some more training in," he added.
"I have a brilliant group of players, a really good team and if we could add to it we would like to do so but not every manager is lucky enough to have millions.
"We may miss out on little bits and pieces but the one thing Everton will be is competitive in the Premier League.
"What we want to do is get ourselves up the league as quickly as we can.
"First of all this year is to get the points to make sure we are not in a relegation situation and then kick on from there."