The Toffees have made a disappointing start to the season, collecting just two points from five Premier League games and crashing out of the Carling Cup at the hands of Brentford.
Moyes believes part of the problem might be that Everton are not showing the sort of fight that has helped make them such awkward opponents in recent years.
The Scottish tactician has now called on his troops to toughen up ahead of Saturday's clash against Fulham and demonstrate more substance than style.
"The biggest concern for me is that we have lost our competitive edge in the last few games," he told the Daily Post.
"The one thing you could never do was beat Everton up.
"If you wanted a scrap against us, then we'd be standing there waiting for you, not a problem.
"I've told them that I've been disappointed with the physical side of their game. Especially against Newcastle, I don't think we've competed as well as we can."
Moyes accepts that it will be difficult to find the right balance because he is proud of the attractive way Everton play their football nowadays.
"Maybe we will have to sacrifice a little of the playing style we have got to get better results," he said.
"But the players we've got here, we can't suddenly go and shell the ball forward, take long bombs into the box. I don't think I've got that style of player.
"We've evolved since I first took over, we don't have that style. We play football, we pass the ball around and we are creative going towards the 18 yard box.
"We have moved forward to where we are now.
"The Mikel Artetas, the Steven Pienaars, the Leon Osmans, we are in a different stage of our development now, and it is certainly not so simple as stopping playing a certain style and switching to another."
Source: Team Talk
Source: Team Talk