Everton's misery after collecting just two points from their opening five Premier League fixtures was compounded as they were dumped out of the Carling Cup by League One Brentford on Tuesday.
Their form has undermined pre-season optimism founded in their superb finish to the last campaign and pressure is growing as they travel to Fulham in search of a much-needed win.
Moyes said: "We started the season with the belief, coming off two defeats in 24 last year, that we would start the season well.
"It didn't happen and that affects your confidence.
"It's disappointing because I didn't expect this. We expected to start better after the good run we had last year.
"We want to do better and nobody cares more than the players, I can see that by their attitude and the way they are training.
"Football pressure is what I do, it is what the players do. It is why we are in the business and we will get on with it."
Everton took just 15 points from their opening 14 games last season and Moyes is frustrated that his team are being labelled as slow starters.
He said: "I wouldn't say you want to prove people wrong but I have been in this situation quite a few times now and it is always the same kind of people who come out and say things.
"We turn it around and they come back again when we don't start the season well.
"But it's a difficult run. Five of the opening nine were away and two of the four at home included Manchester United and Liverpool.
"I knew this start was going to be quite a hard one if we didn't get off to a good start against Blackburn and Wolves."
The midweek result was embarrassing but Moyes was confident the players would soon get that out of their system and was more concerned with the performance in last week's league loss to Newcastle.
The Scot said: "We have really moved on, we have been in Thursday and Friday preparing the players.
"We could have scored five or six and if we had nobody could have said anything.
"We should have gone through but we have to give credit to Brentford because they are a lower league side and they hung in there and stuck with it.
"We just couldn't score, we didn't do enough in that final third to make it easy in front of goal.
"We have got to try to create as many chances at Fulham and let's hope we take some of those chances.
"We might need a bit of luck to get us off to a start but I can't fault the players, Newcastle apart. That was our worst performance since Hull last November.
"We have been looking to win and no one can say we've not."
The lack of goals from strikers is a concern for Moyes.
Louis Saha is currently sidelined with a calf injury and Yakubu has not regained full form and sharpness since the World Cup.
Victor Anichebe has not been an option yet this season due to a knee injury and has now been told he needs an operation.
That has heaped pressure on new signing Jermaine Beckford, who is trying to make his mark after stepping up from League One.
Tim Cahill played in an advanced role in the 3-3 draw with Manchester United a fortnight ago but is rated only 50-50 for Fulham after two games out with a knee injury.
For all their composure on the ball, Moyes also feels his team need to add a bit of bite.
He said: "We try to keep our discipline in check but one of the things I would say to the players is we need to see a more competitive team at this present time.
"There have been a couple of games, Newcastle especially, where we didn't compete as we would have in the past.
"I won't accept that."
Source: Team Talk
Source: Team Talk